No, if you have a high deductible plan, you pay whatever the hospital negotiated with your insurance company. When they talk about underinsured they mean (normally) those with plans that don't cover normal treatments. For example, a treatment I used to get for my back pain was covered under my previous insurance, costing about $100 for the visit and injection. Now that it is not covered the only doctor that will take me charges over $500 for the same injection.