Honestly, it's my experience that no matter which Insurance company you deal with that you'll be sure to find this. That's their business and how they make money. The goal of insurance is to pay for something you hope you never need, and if you do it's there. You're not going to find a company that WANTS to pay you and take out of their bottom line. I've never had anything denied by State Farm but I've never had anything catastrophic either, so I can't speak from that perspective.
I'd be curious to know what they didn't pay and why though and would bet it was within their right not to pay what wasn't paid. I wouldn't wish that on anyone, but since this is something that we want to be there and hope it never is, we don't usually read all the policy details as they make them as confusing as possible and likely there was something in there that excused their liability.
It sucks, but they are there to take out money and pay out less than they take. Maybe if you can find a non-profit insurance company, but I don't know if there are any of those. I just did a search and all I got was insurance FOR nonprofits. I hate search engines these days and think they've gotten really sucky but that's a whole other topic.