A reputable company will do what they can to avoid paying false claims, but will not hesitate to pay legitimate claims. Anytime they refuse to pay on a legitimate claim they lose a customer and get that former customer complaining to all his friends about the poor treatment he received from the company.
The amount of advertising by Progressive and Geico makes me wonder if their approach may tend toward a willingness to cheat their customers on legitimate claims. They may figure that the advertising is a necessary cost to continually replace the customers they lose.
As a rule of thumb, I usually assume that the less advertising a company does, the more likely that the company emphasizes keeping existing customers happy instead of having to find ways of replacing the ones that left. The guy that did the roofing on my house does no advertising at all. Not even a yellow pages ad or a listing in the newspaper. His customers all come from word of mouth referrals, and he's always got more work than he can handle.
Name a reputable insurance company that has not committed fraud and or been in violation of law.