OP here. I explained the situation early on in the thread. My insurance broker said that I should try and prevent them making a claim as the insurance company might just pay it rather than fight it and I would be left to pay my $2500 deductible. Shitty advice, and maybe it's time to find a new broker.
Unfortunately, I am the one who has to deal with this. I know all the players involved, I have all the evidence and I can explain it in a way that makes sense. If I just hand it off to some random insurance company employee they may not be motivated enough or care enough to put the effort into fighting it.
Also, I still haven't been served with anything. Once I get served I still have the option of telling my insurance company about it. I most likely will. Think what you want, but I have successfully dissuaded two law firms so far.