It's more like the your renter's insurance company would sue the neighbor's company for a claim. However, since the neighbor was renting out the apartment as an Airbnb property, then their standard renter's insurance was probably invalid at the time. So now your insurance company would sue the neighbor directly and may not be able to pay.
The long term implications are that renter's insurance costs will go up for everyone in that market.
I've long thought that the biggest problem with Airbnb wasn't the tax issue, or even landlords abusing the system and running mini-hotels. It was insurance. I suspect that none of the hosts who aren't physically present (and even some who are) are violating their insurance policy, and if there is a HOA or other sort of shared space, that insurance policy would also be violated.
If hosts had to actually pay the true costs of insurance, the cost savings between traditional hotels and Airbnb would be much smaller. Now, if Airbnb actually offered the insurance to the hosts, or maintained it themselves, that would be something. But that would be fraught with fraud issues over such a wide market.
But insurance isn't a sexy topic...
(I like Airbnb but see how fraught it is, too).