Yes and no . . .
You and I might have known how to disect a freshly-killed frog in high school. And we would have been able to identify all the organs, pretty much.
But would you know how to restart its heart?
Now, how about a fish? Or even a fellow mammal. Where is cat's heart? What drugs would you use? What dose? How much voltage for the paddles (which McCoy did not have handy)? Let's say you even happen to be a suburban vet. But what if the patient is a tiger? Have you ever had any training in exotic animal care?
Now, how about another species from another planet?
I think McCoy can be forgiven for knowing a lot about Klingons, but not knowing how to restart an alien heart inside a bleeding chest cavity.