According to Weird Al's interview on TheForce.Net, he managed to gather most of the advance intelligence from the Internet:
The song was entirely based on Internet "rumors." I gathered all the
leaked info I could about the movie from all the various Star Wars
websites (TheForce.net was particularly helpful), and was able to
piece together the basic plot of the movie. We had planned to release
my "Running With Scissors" album the month after "Phantom Menace" came
out. But because of the lead time involved in recording, mixing,
pressing, and physically getting an album out in the stores, I had to
write "The Saga Begins" about two months before the movie came out.
The folks at Lucasfilm have always been very friendly towards me, but
they politely declined my requests for an advance screening or a peek
at the script. Thankfully, the storyline according to the Internet
followed the filmed storyline pretty accurately. Just for safety's
sake, we didn't do the final mix on "The Saga Begins" until after I
had seen the movie (I paid to go to the $500-a-ticket charity
screening, so I could see the film a couple days before the rest of
the world). I remember I changed a couple lines after seeing the movie
- very minor tweaks. Like "He's probably gonna marry her someday" was originally "I HEAR he's gonna marry her someday," because according to
an Internet rumor, in one scene Anakin tells the Queen to her face
that he's going to marry her (which, as it turns out, wasn't in the
final cut - but everybody knows how the storyline is going to go
anyway, right?)
