They still can profit massively from that, though, so it's still kind of messy territory.
A grey area would be more like whether you should offer to leave the meeting while they discuss the proposal.
Of course, the conflict definitely needs to be disclosed!
Per the peer comment, if you don't disclose the conflict, and let the BoD decide what to do in light of that conflict, then you're into the realm of looking like you're hiding something.
Are there even laws for this, or is it more about company policies set by the BoD?
In addition to generic criminal laws against fraud and bribery there’s also honest services fraud (which I’ve mentioned elsewhere in this thread) which boils down to depriving someone to whom you owe a duty of the right to your honest services.