How would publishing a paper open a 3rd party up to legal risk? Research papers aren't laws, and it is chronologically impossible for a research paper to influence already on the book laws.
I can imagine a scenario where a politician who wants to pick a fight with Google uses some of the unflattering findings in the published work as supporting material for why Google needs to be regulated/fined/etc: "Google does {bad thing}. Look at this research report from Google researchers! They admit to doing {bad thing}!"
A paper from Google saying that Google knows that its systems discriminate against minority groups can open Google up to liability for a class action lawsuit from said minority groups against Google. And the fact that Google knows increases the damages that they can look for.
The same paper from outside of Google also creates liability, but now the argument for increased damages becomes about whether Google knew.
That would be more of a journalistic paper than a research paper then. Timnit's research, at least in the past, is along the lines of "Hey, this <thing you thought benign> is not actually benign"
