I can't see that you have an obligation to do this. They need to prove that you are the person who owes them money. You might try working your way up the chain of command if you aren't having success with the billing dept.

I have done this, but they still insist that I give them my SSN and driver's license number, but I don't trust them. Why would I after all, seeing as how they do not reciprocate?

Technically they should have to prove that you are, but that doesn't mean that they might not try to report you. You're better off persuading them to look elsewhere for the right person. Definitely don't give them your SSN or any other information that is not public.

My advice would be to contact someone in the hospital billing department and explain to them that you aren't the person who received the services.

I'm not sure I understand the question but if you've defaulted on a hospital or clinic bill, I wouldn't risk hoping the don't report the collection to the bureaus just because you didn't provide a social security number.

It's not actually my debt to pay. The person has the same name, but they are trying to collect personal info from me as if I were the one who had used their services.