Our one experience with a ships medical staff and facilities was the single most dissapointing moment on any cruise ship. We visited the infirmary on the Fantasy after my wife banged her knee on a shore excursion. From the moment we walked in, they were rude and uncaring. The nurse at the desk scolded us for "showing up 20 minutes before they closed". Then the doctor told us that if she hit her knee and it hurt enough to come to the infirmary, then we should have just gone to a hospital in Cozumel. Their facility didn't appear to be set up to handle anything more than handing out sea sickness meds. Their only other function seemed to be to make sure our injury would not lead to any form of litigation in the future against Carnival.
They didn't even have a small portable x-ray machine. I agree with Kuki that the doctors onboard are probably not up the standard we have practicing in here in the US.
I really expected a better experience and much better facilities. Lessons I learned from this are (1) that you never travel without insurance (I never have before and this just reinforced that). (2) Remember that a cruise line is a business and they will always cover their own tail. (3) A ships infirmary is nothing more than a small town clinic with VERY limited resources and abilities.