This doesn't appear to be true. There are other ways for health insurance companies to increase profits.

The US Health insurance industry spends on average, 86% of premiums on healthcare costs[0], which means they can increase their profits by reducing those costs, since 80% is the floor.

12% of the left over premium gets spent on operating expenses, which leaves the industry with a 2-3% profit margin[0]. So another way of increasing profits is for the companies to become more efficient.

These figures are for the industry as a whole. Any individual company will have other avenues of increasing profit, such as growing their market share.

[0] https://content.naic.org/sites/default/files/inline-files/20...