@Jason G. Thanks again for all the info. I spoke to my insurance agent, and he basically said everything you've pointed out. Judging off the letter, he thinks it's bogus too, but admits that the carrier will look at all the facts before deciding how to proceed. At a minimum, it sounds like the carrier will force the lawyer to file a lawsuit...and that could result in the lawyer dropping the case. But if not, it'll probably be months before we hear anything else.
Sidenote: Assuming this is a scam, I don't understand how there aren't laws in place to protect against this. A simple law making personal injury lawyers accountable for court costs - should they lose - would be enough to dissuade a lot of these guys from taking crap cases. My understanding is that it's very difficult to win these cases in my local court system, but because it's at least 10-15k to defend an average claim, it rarely makes sense to fight it. Most of these lawyers only sue for an amount similar to what they know it'll cost the insurance agencies to fight. And the cycle just goes round and round.
Regarding the insurance premium, my agent said that if I continue setting up separate LLCs for each investment property, there'd be no impact of this claim on future insurance coverage. My GC, however, might see an increase if the claim goes against his insurance...but if so, I'm sure he'll find a way to pass that extra cost onto me!