Doctors and Nurses

Do you remember, when we were kids - we used to play 'doctors and nurses'?
And despite our young age, we naturally managed to introduce the faintest shade of naughtiness in our otherwise innocent game.
But now, when I am older and wiser (as the saying goes...), I am wondering. If the 'doctors' always went to give a more or less thorough examination (wink, wink), then why were they doing so to the nurses?! Usually doctors examine patients. Philosophically speaking, if a nurse is being examined by a doctor (ahem), then she would become a patient - for the sake of the argument.
So why wasn't the game called 'doctors and patients'??

PS: On a different note, it happens that I work with both - doctors AND nurses. And I like to play games too. So damn, I am in the wrong job then! I should train to become at least a nurse.