For reference on the no training side:
Dr. Dre and Dr. Venture: Both possess honorary doctorates. The former from UCLA, the latter from a Tijuana community college.
Dr. Pepper: Charles T. Pepper did have a medical doctorate. He is cited as a possible source of the name.
Dr. Evil: Evil medical school.
Zoidberg: Claims he lost it in a volcano, more likely a art history degree.
Dr. Horrible: Likely physics though he claims Horribleness (though it could be a catchphrase.)
Dr. Seuss: Intended to get a Doctorate of Philosophy, got an honorary doctorate of Humane Letters.
The Doctor: Per This - While pretending to be the Doctor in an effort to save herself from an army of Cybermen, one of the planet’s deadliest enemies, in Death in Heaven, Clara said: ‘I don’t even really have a doctorate. Well Glasgow University, but then I accidentally graduated in the wrong century.’
Doc: Does become a doctor at Storybrooke hospital in a live action show, “Once Upon a Time”, apparently not a surgeon though.
Spin Doctors: No doctors.
I feel like a fair amount of those on the trained side aren’t medical doctors (Phil, Ock, Robotnik, Lector, Honeydew) or at the very least, aren’t folks you’d want around for your heart attack.
It’s shitty… but I get it. We already know the kind of petty craven asshole he is, hedging your bets in case he wins so he doesn’t shit all over you is a good play in theory. In practice he’ll still do it if you so much as hinted his shit didn’t smell like fresh strawberries, so why not go in guns blazing?