That was what I was thinking at first too, but if I was sitting on their side, my mind would still go for "Wait, if we sue him, won't this make the news and make things better for him?" immediately, rather than "Yeah, this will suck for him". I'm not sure how they thought this would be bad for him, legal costs?
You're assuming a rational, reasoned process, rather than an instinctive punishment of a perceived status challenge.
When you observe someone acting in a way that seems obviously against their self-interest, it is always worth considering the possibility that there's some interest you don't understand...but it's also worth considering the possibility that they're doing a bad job of considering their own interests.