Regarding Chapel's rank, it would probably be a good idea to consider her an Ensign during TOS. While her rank is never mentioned or put in braiding during that show, TAS gives her a single Lieutenant braid on her long-sleeved uniform, and confirms this with an ID card spelling "Lieutenant" out'n'loud in "Mudd's Passion". Yet she clearly remains a nurse there.
Thus, the officer rank shouldn't be argued to have been due to her achieving a Doctor's degree, but should be something she already carried while nurse, most probably in TOS as well as TAS.
We have met several pipless, enlisted nurses or medtechs in the TNG era where Ensigns stand out clearly due to their collar pips. Yet the prominent head nurse of Dr. Crusher, Nurse Ogawa, was an Ensign.