My son is 20 and they ask me to sign the insurance form as the main insured. I don't know if it varies by state. Colleges also offer insurance to kids for minimal amount and that, they don't need the parents to sign the insurance form when seen in the clinic or hospital.
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I don't know Smackie... My son goes to college in my State and he can go alone to his pediatrician because they have my insurance file with them. But if he needs to be referred to a specialist, they make him sign a form and I also have to sign the same form being the main policy holder. We've never Been in a situation where he was out of state and got sick, so I really don't know how it works.
But like starnique had mentioned, if he went to a public hospital or clinic, he will pay a very small fee to be seen by MD and they keep everything confidential.