First off, the hospital is not the one reporting to your credit report...it's a collection agency for the hospital. From what I gather (and someone chime in if I am wrong), hospitals can not report to credit reporting agencies, only the collection agency can.
This is from my experience, and YMMV, but when I had a medical collection pop up on my credit report, I immediately called the hospital. It was actually a duplicate billing issue, but the representative told me I would have to pay the collection agency. Knowing it was a duplicate bill, I disputed the collection account with each credit reporting agency and sent a DV to the collection agency. A week later, I received a letter from the collection agency that the account was removed from my credit reports. And it was!
As long as you paid the hospital and have a receipt or other verification of payment, I would DV the collection agency and dispute the collection account with the credit reporting agencies. If the collection agency can't verify the account, it must be removed. And since you've paid the amount to the hospital, the collection agency should not have any reason to verify or validate. Worked for me.
However, you may want to search for HIPAA laws just to be safe. 