No gain, all liability. Easier to cut them a check for access to training data and say nothing. Unless legal discovery was performed, the outside world would never know, and the payment records would roll off corporate records through a record retention schedule eventually. Could obfuscate it as a contractor consulting fee ("knowledge management subject matter expert") if you wanted to get tricky, depending on the risk appetite of whomever would receive the funds.
(not legal advice!)
There’s zero liability in a company stating publicly that they support Anna’s Archive. Zero. Free speech protections cover much more egregious statements than that.