My response to that is that yes, that can happen, but in a system where you actually have a competitive market, there is an incentive for insurance companies to pay out benefits, or else they won't stay in business. Unlike with modern health insurance that people are basically forced to have, the old "in case of a big emergency only" policies weren't required. If the company didn't have a reputation for paying out on policies when needed, people just didn't buy them. And, the insurance companies mainly made their profit off of not paying out at all for the majority of people who never made a claim, rather than off of rejecting legitimate claims.

Although, to be fair, these policies may no longer be workable in today's environment of chronic disease. They seemed better designed to serve a baseline healthier population.