That's an odd thing to call a "fact". We're confident of this because of her uniform braid?
The braid is the only evidence we have, and there's nothing to refute it. If you're not convinced it's probative, then fine, it's easy enough to phrase the clarification in a way that acknowledges the uncertainty. E.g. "There was never a female guest star that definitively played a character higher in rank than Lieutenant in Starfleet; the one possible exception is Diana Muldaur's Dr. Anne Mulhall in 'Return to Tomorrow,' who wore lieutenant commander's stripes but was never addressed by rank." Although I see no reason to be so skeptical of the rank stripes. Just because something is an exception to the expected pattern doesn't mean it can't be true.
Is it possible they just threw her in a uniform, and weren't very careful about what the number of stripes meant?
That seems highly unlikely, for the very fact that we'd never seen a female lieutenant commander before, so they wouldn't have already had a suitable uniform lying around. If they'd just slapped on something that was already available, they would've put her in something with lieutenant's stripes or no stripes at all, because those were the only female uniform options they'd ever had before. So a female uniform with lieutenant commander's stripes is unique, something that would've had to be made specifically. I can't see how that could've been an accident.
To me, there are problems with either assertion about her rank. Her wardrobe argues against her being a "mere" lieutenant or lower, as you observed. But Kirk's bewildered "Who are you?" to her in the transporter room argues quite strongly against her being a lieutenant commander. I find it hard to imagine Kirk being unaware of anyone on board the same rank as Scotty & McCoy – much harder to imagine than the wardrobe dept screwing up the actor's braid.
He may not have known her by sight, but that doesn't mean he wasn't aware of her. After all, he hadn't summoned her to the transporter room; his "who are you?" could have simply meant that he wasn't expecting to see her there and didn't immediately place her by sight alone.
Not to mention, of course, that there had to be a way for her to be introduced to the audience. Exposition is often provided in contrived ways, and having the captain not remember a character's name is a way to provide it. Cf. Helen Noel and Marla McGivers. So I don't think the line had anything to do with the writers' intention regarding her rank, just with "How do we introduce this character to the audience while also establishing that Kirk didn't request her presence?"
EDIT: Oh, and one more thing: The James Blish adaptation of the episode does introduce her as "Lieutenant Commander Anne Mulhall." Although that adaptation was published in 1973 and thus probably written in 1972, late enough to be influenced by seeing reruns of the episode, so that doesn't necessarily confirm that it was in the script. It's suggestive, though.
Berman was always a company man, and this is the primary reason why I dislike him so much, aside from the fact that he went out of his way to undo all of the "canon" of TOS Trek, like Zephran Cochran coming from Earth...
Umm, there's a ton in "Metamorphosis" that makes it crystal-clear that Cochrane was an Earth human. McCoy explicitly says "He's human, Jim." Nancy/Companion later says "Now we are human." Cochrane is very intolerant of anything "inhuman" at first. Cochrane says the planetoid is "not Earth, but it's liveable," and the Companion made it duplicate Earth conditions for his benefit. Despite the "Zefram Cochrane of Alpha Centauri" line, it's obvious that Cochrane was of Earth human origin, and since he's the guy who invented interstellar drive, the clear implication is that he was meant to have been born on Earth and later moved to Alpha Centauri. Any fans who actually paid attention to the episode have known that for 47 years; the belief in some fan circles that Cochrane was from some native Alpha Centaurian species that happened to be identical to humans was always a silly, wrongheaded notion based on a misremembering of the actual dialogue in the episode.
I think it's safe to say "no." If you go by what's onscreen, two stripers Spock, Finney and Giotto are all lieutenant commanders, just like Scotty and McCoy with a stripe-and-a-half.
Spock was only referred to as a lieutenant commander a couple of times in the first season, and Finney and Giotto were from the first season as well. In seasons 2 and 3, Spock was consistently called a commander, matching his braid. The use of braids had become standardized (and Spock had been promoted, evidently) by season 2.
ETA: The '70s Technical Manual wasn't right, either, IIRC they left out lieutenant JG and the commodore stripes weren't like the ones seen in the show.
The lieutenant JG rank was never used in
Star Trek prior to TNG.
The one and only female Starfleet officer in TOS portrayed with a rank higher than lieutenant never had her rank stated in dialogue.
