This is an interesting question as it's one I have encountered multiple times in entirely different settings. I've been to court before (and won, without any help), so am well aware of just how evidence based the process is in reality. On TV it usually comes down to who can bang on the desk or shout enough. In reality, it's almost entirely reading through receipts, looking at letters, paperwork, proofs of postage etc. The success or failure of your case can come entirely down to whether or not you can actually produce some form of 'solid' evidence as opposed to just your own account of things.
There are certain people or organisations that will always attempt to avoid putting anything down on paper or in an email as it potentially renders them liable in some form or another. This is not only in a legal sense, some people won't do it purely for the potential (and sometimes very trivial) reputation damage it could do; e.g. if they're supposed to be supervising something yet make an incorrect or poor suggestion.
After my exposure to court and various other anomalies, I've taken the approach of hanging onto at least one copy of anything remotely official. If I had a scanner, I would also scan these. It seems time consuming but it's actually really simple to just drop things into the folder when they turn up and it has actually been useful; e.g. I managed to reproduce three different voting registration confirmations from there for the bank.
I have also worked in the pharma R&D sector which is heavily dominated by paperwork and chains of custody. Anything and everything that is done (scientifically) is supposed to have at least one piece of paper associated with it.
There is an immense amount of rank pulling and avoiding of stepping on toes. E.g. I frequently watched people doing things (as the most junior member of staff) that were categorically incorrect (such as writing down what a volume should be as opposed to what it actually is) or that would potentially be picked up by the FDA as inappropriate. But basically nothing was ever said because people didn't want to get into arguments with the other people they'd spent 15, 20, 25 years working with and would be stuck in the office with.
As the most junior member of staff, I also frequently observed people attempting to hand off blame in my direction. For instance, I could be sat at the desk with a person either side of me handing me their own paperwork to countersign against some unknown error they'd decided had to be something to do with my involvement; with precisely zero scientific basis behind it or truth. As a for instance, I watched a senior scientist spend three months running one analysis that should have taken two weeks, and generate over two hundred results for it when it should have only required around 20, the entire time with a fault message ('heater not functioning') they didn't understand appearing on the front of the equipment (a point I raised, three times, and that was ignored, three times). This alone resulted in a three month long argument between departments about why the results of the tests where all over the place. Again, one of the outcomes of this situation was (for the one or two tests I was partly involved in) to have me sign off on it essentially being down to me 'not mixing something enough'. Which they not only didn't have any actual evidence of (because it wasn't true) but obviously wasn't the problem because the error was there before and after my temporary involvement. They then attempted to imply it may be due to me tampering with equipment; which was me emptying a bottle on the machine, that they'd asked me to empty. There were sheets of countersigned paper in the files dedicated to the errors I'd solely made, after asking three or four different senior members of staff what should be done, minus their names, a statement that I'd been reminded this wasn't company policy, and then their own name at the end next to the correct set of outcomes. Ironically, given that they were highly reluctant to let me work on any regulated work, they were fine with me fixing broken bits of equipment (e.g. they'd managed to pull a signal lead out of it's screw terminals on the back of a detector dragging the equipment around and between them and the manufacturer couldn't figured out how to reconnect the two wires due to a major breakdown of communication). Technically, the heater fault should have been investigated as soon as it appeared and I shouldn't really have been fixing the wires as I wasn't technically trained, signed off (or paid) to repair anything at all (and this piece of equipment was being used for 'regulated studies', i.e. those that might form the basis of an application or support profile, so the results it generates could be considered direct legal evidence). They were literally just guessing at what could be wrong and randomly trying different things to see what would work, not only my own supervisors but also their own (people with 'decades of experience' in analytical science).
This happened endlessly, they weren't one offs. It was a culture of 'if you can pass the blame along, do so'. As another example, my own supervisors made liberal use of the flexible hours policy. In so much as they would often turn up at 10 or 11am then have left by 2 or 3pm or in some cases both take what seemed to be un-noted mini holidays to the point that I was left entirely in charge of handling requests, collecting samples and sending results out. The study directors ended up coming to me as a primary contact point to ask about changing study protocols because they'd only ever get arguing with the others. This was pointless in some instances as I wasn't approved to request any service or material or make any changes whatsoever to any protocol.
They also had a habit of putting things down in an email after deciding what to do. And would purposefully avoid saying 'we decided this' or 'this should be done' but would go with 'what was suggested' etc without discussing what it was that was suggested.
I would highly recommended adding a call recorder to your phone just in general.
As dire as it sounds, I have even looked into wearing some form of voice recorder when in such an environment just in case something gets said 'off the record' that turns out to actually be 'on the record' when it turns out to cause a problem. This is effectively the nuclear option you would only want to use in a serious situation; e.g. someone trying to fire or formally warn you for something they told you to do.
There is essentially no way to fix many of these problems. You can sometimes make suggestions (which they will likely take personal offense to) or attempt to force the chain of custody by replying with what will be done and how and asking them if its what they meant but that's likely going to need doing any and every time and will eventually be seen as being argumentative.
Eyal is correct that keeping some form of note book of what's going on could be useful however it's not actually very good evidence at all really. A court might consider that, or if you contact a different (and preferably higher) manager they might be interested, but they might also see it as being disruptive; as an example, someone attempted to warn the company I was working for of inappropriate sales strategies being used by some representatives and were then made redundant for having a poor team work mentality (the company was later found guilty of criminal activity, fined a few billion dollars for related problems and everyone within the company was forced to undertake anti-bribery and corruption training, yearly). In the long haul, your own account of things won't actually carry very much weight at all either in a company or in a court. If you only email out what you're going to do, or think has been suggested, and get no 'okay, that is correct', they can just as easily say you weren't ever told to do what's in the email; that you've just assumed it to be correct.
Given that your manager has specifically told you not to ask for any emails, it seems quite clear that they are specifically trying to avoid taking any responsibility at all and are almost certainly aware of what sending such emails can mean; that they may have to take some responsibility at some point. Hanging up the phone is ridiculous and, in combination with the emails, an almost sure sign they are purposefully avoiding any kind of record involving them.
I think life is too short to put up with that as it's essentially a form of soft slavery; they get more than you because they're supposed to be solving problems and taking some extra responsibility for getting them solved, not creating them and then trying to blame other people. If it's built into your department or the company structure, the best solution is to look at changing departments or jobs.
