Until (or if) H.R. 2086 passes then paying a collector won't guarantee that it will be removed from your credit reports. If it does pass then the collector must remove the debt from your credit reports upon payment. But don't hold your breath since it seems to be stalled in the House at this time.
Paying the debt 'in full' to the HIPAA Compliance Office at the hospital would get it off of your reports because of HIPAA, the FACT Act, the HITECH Act, the FCRA, your states Privacy Act, etc. Once the original medical provider is paid in full then there is no longer any permissible business purpose for the debt to remain on your reports or to remain with the collection agency. The collector would be required to return the debt to the hospital, remove everything in their files concerning it and remove it from your credit reports.
You might go to the free site I've listed in the source box and do some reading in the Medical Forum. You'll be able to find a step by step guide, with sample letter templates, in paying the hospital and using your rights under the laws I'd stated above. The site is totally free to read, use anything you find on it and to ask any questions you may have. The step by step guide is also free to use.