The legal reason isn't that they aren't allowed to, it is that it can only hurt them.

Why would a company highlight failures if they don't have to? Especially when their statements can later be used against them in civil or criminal proceedings.

I'm almost certain that FMLA, ADA, etc have provisions that require the employer to treat the information as confidential. Even things like contact tracing for covid keeps the person anonymous.

This is the company that released a video of a bunch of their rockets exploding, "How not to land an orbital rocket booster". They are usually pretty open with their failures, at least in engineering. https://www.youtube.com/watch?v=bvim4rsNHkQ

I guess I didn't specify that "failure of an experimental rocket for a company developing new rockets" is a different category than "failure of workplace safety procedures that permanently disables a family man"

I thought the difference was clear

the difference is clear to be sure, just pointing out that at least in engineering, they have never been shy to publicize their failures, and use them to improve processes. I would hope that that attitude would apply equally to safety, but it seems like it does not.