I think the first step in this situation is for someone from the research project to speak to the company to see if there's a way to publish part of the data with their consent. Here's why: Mary from Acme company wants to work with Local University. Mary knows that some of the information he gives Local will be confidential, so she asks the legal department what to do. Legal doesn't know (or care) much about the project, so they send Mary a standard NDA. Without giving it any more though, Mary asks Local to sign it. However, there may be a way to publish the information in some form that would satisfy Acme, Mary, and the legal department.
For example, suppose Acme is a telecomms company, and you are studying their mobile network. Acme doesn't want the public to know where all their network equipment is, the traffic patterns on their network, or the network failures they've had. However, if you topologically transform the network diagram so that no one can tell where the real network was, and don't mention Acme in the paper, they may be fine with that.
Or maybe Acme is a hospital that shared patient records with you for research. Naturally they are concerned about patient confidentiality. But perhaps the data can be anonymised (removing names, addresses, etc.) to Acme's satisfaction.
So depending on your relationship with Mary and Acme, it may be no harm to ask if there's a way to publish. If you've done good research for Mary, she may be willing to explain the situation to her legal department and get approval for the publication.