Is it safe to assume that potential pathogens are only present on the surface of animal meats?

If we're talking about examined meats that come from certified source then I would say yes. With a caveat - everything that have interaction with air should be treated as "surface". So if you buy gutted fish the "inside" should be treated as surface. Same with turkey (or chicken) for stuffing.

No, this is a feature primarily of beef, some wild game, and poultry. Meats like pork and many kinds of fish may contain parasites and thus need to be cooked to higher temperatures than eg beef or duck (pork) or frozen before cooking (many kinds of fish) to minimise the risk of illness.