Creditors can always sue you to collect a debt. Did you buy into some urban legend that claims a creditor can't sue you for a medical debt or that a debt collector can't sue? Because that is mere wishful thinking.
Hope this perspective helps!
Maybe someone can sue, but it isn't clear from your facts who. If the debt collector was HIRED by the medical provider to provide collection services, they don't have the authority to decide to sue. Any implication that they will make the decision to sue is likely against the law.
If the collector BOUGHT the debt, than they do have the authority to sue. However, whenever any debt collector except for the original creditor tries to collect, they must send documents validating their right to collect. If they bought the debt, this would include the contract for sale of the debt. If they haven't validated, you can sue them.
One final scenario, since you say you don't believe you owe the debt. Recently, I've come across a disturbing trend where people who are no longer working for a debt collector make copies of their former employer's files before leaving the company, and then use the information to attempt to collect debts and keep all the money for themselves. Here, you may have claims in addition to the debt collection practices laws.
Regardless, you should immediately contact an attorney who does debt defense and FDCPA work. You can use the Avvo Find a Lawyer, the National Association of Consumer Advocates' (NACA's) directory, or if you can't find anyone even with that you could consult with a local bankruptcy attorney, as they usually either handle these suits or know someone who does.
My response to this question does not mean I agree to represent you in any proceedings. This information is also not subject to attorney-client privilege.
If this is a debt that you did receive treatment for, then they can sue. I'd meet with a BK lawyer that gives free consults. My firm would be happy to talk to you at no charge.