I don't know why, but it seems a good-sized post I made in reply to Bjorn got eaten by Shub-Internet.
Ah well.
King just plain cannot be a genuine, traditionally-trained Muay Thai fighter. We've seen her with her shirt off, and she noticeably lacks the abs any traditional Muay Thai fighter will always have. She also kicks wrong (doesn't lock the knee and swinf from the hip often), and seldom uses elbows or knees.
Even if you discarded the whole "no wimmenz allowed" bit, she has none of the marks of a traditional Muay Thai user. Most likely, she learned the sport-oriented kickboxing form, and has just been supplementing it with stuff she picked up during her years as a bouncer and a KOF participant.
Look at the real Muay Thai fighters in the Street Fighter and King of Fighters worlds (which are not canonically connected, by the way, so you picked a bad example).
Joe Higashi. Sagat. Adon. All three are scarred, tanned, and muscled to hell and back. Look at their abs, thigh muscles, and their protruding shin bones - old-school Muay Thai trains students for years to achieve these, and with good reason.
Without the strong bones and leg muscles, they'd never be able to deliver the devastating low kicks Muay Thai is famous for, nor would they be able to withstand them from their training partners. Without the insanely toned abdominal muscles, they'd never be able to survive the brutal beatings that accompany Muay Thai training without losing a few organs.
Real Muay Thai is a killer's art. The traditional fights allow for maiming and killing as viable means of defeating an opponent. Thus, all old-school MT promotions are essentially restricted pit fights, run by criminals. Sagat was already a criminal before entering Shadoloo, just for that reason.
The pride these warriors have is pretty well justified; they took on opponents who were not required to think about their opponent's safety, and they not only survived, they became champions in their own right. There's a lot of pride that comes with that. All three of them have since progressed beyond what the traditional MT teaches, but that pride in their roots will likely never leave them.
Adon, being a more traditional MT user, demonstrates his pride by applying those old-school Muay Thai techniques to a tournament which has no such restrictions. Granted, he never wins the tournaments, but he's up against the stiffest competition in the world (including his former mentor, Sagat, the Muay Thai Emperor himself) - it's saying a lot that he doesn't get himself killed in action.
Joe Higashi is probably the farthest shot from tradition, as he is seen to not only add straight punches and snap-kicks (which are never used in pure MT), but to be rather crude, vulgar, and careless in battle. (Mooning the opponent...) Yet, his Tiger Kick - a souped-up kao loi, the jumping knee used as a knockout blow - is a clear shot to his roots.
Sagat is the man of the hour, though. He also incorporates some straight punches (jabs, the Tiger Shot, and the Tiger Uppercut among them), and has been known to use high kicks - something rarely done in Muay Thai. His mastery of the Tiger Knee alone is enough to prove his pride in his roots. I'd wager the unconventional additions were, like the Tiger Blow (made to imitate, and hopefully surpass the Shoryuken), created so that he could adapt to the greater challenges in the world circuit.
Seriously, man, old-school Muay Thai warriors take their traditions seriously. You'd never find a traditional MT teacher training a female student.