Nothing you said makes my statement untrue.
Even if an insurance company has claims greater than its premiums it could exist, and even be profitable, because of its ability to earn additional revenue through investing its float. You seemed to omit this consideration, which is significant because investment returns on billions of dollars can be significant.
I think you're correct in a very specific technical sense (measuring in nominal dollars, that is), but not in the sense that matters in the real world.