Is it illegal if you don't inform a medical care provider of health insurance?

Let's say you have health insurance, however, your insurance is so awful that's it's nearly impossible to find the needed doctors. Can you go to a free clinic and use a sliding fee scale? Is it illegal not to tell the doctor of your health insurance coverage?
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I'm not sure if it's illegal, but it's not right. If they do ask specifically about insurance and you lie, then that may be something that breaks a law. If they don't ask, perhaps you haven't technically broken the law. If you have a bad policy, you still have a policy and the provider MIGHT be able to get some kind of reimbursement from them. Otherwise, you're limiting what they can potentially obtain for services and that means their budget doesn't stretch that much farther. When my father has used the VA, they know he is on Medicare, so they bill Medicare for some of their services. As is, the VA is given $x and it's not nearly enough to treat all those who served, so they have to RATION care and they have to try to recoup expenses when they can. Any clinic you'd be seeing with a sliding-fee scale is in the same boat.
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