I'm a claims guy. Poor maintenance and wear and tear aren't insurable. Like you wouldn't file an insurance claim on your car if the engine seized up due to never changing the oil. Same applies for airplanes. It's spelled out in your policy, so as long as it fits the definition of an unforseen occurrence(birdstrike, you run your car into the wing, you gear up) it is usually covered(trying to speak in general terms since every company's policies are slightly different).
Of course insurance companies don't want to pay claims but that is why you have insurance. But the burden falls largely on the underwriters to write good business with a low risk of claims, or adjust premium to cover those inevitable ones. The negative perception of insurance comes from health and homeowners insurance. Aviation is much different. If we deny claims without basis we get in trouble with the state commissions(don't have deep pockets and lobbyists to sway politicians) and lose customers. Why would we do that? It's cutthroat as it is, so bad claims services is a non-starter.
I can't think of one legitimate claim I've denied. And I've paid from everything from dogstrikes, birdstrikes, lightning strikes, to smoking craters, to taxiing into a post on a car zipper lane, to ingested mats left on the wings of jets. I've handed over total loss checks for jets, helicopters, down to $300k pistons when the pilot balled it up due to leaving brakes on, gear up, ground looped, on and on. Human error is certainly covered. Now, if you were required per the policy to be typed/current/1000 hrs in type etc but you didn't meet those requirements and had an accident directly related to that, there could be an issue. But I've only seen that one or two times.
And yes, I swoop in with a bag of cash in our company airplane and make it better.