Both are equally bad in that situation. If he effectively saved her without detrimental effects, why would she complain? Because it isn't feministically correct?
Lots of reasons the FMC might not want to be 'rescued' by the male.
Maybe she's about to talk her way out of the situation. Maybe she knows one of the mob organizers, the local policeman, or a local citizen of some repute. Maybe she was about to run like hell, and the MMC attracted so much attention in her direction that she couldn't. Maybe she's a photojournalist and Risking Her Life to get pictures the MMC just jettisoned.
What I'm saying is, the author can write a rescue scene and carefully adjust the amount of gratitude this produces. It's author's choice.
. She can't realistically get out on herself if she's just an ordinary person who doesn't know karate or kung fu, or whatever and doesn't have a gun.
The author can give her karate. The author can put a Luger in her jeans. One can't just say -- she's a woman so she's incapable. It is authorial choice.
... suddenly they're two.
I dunnoh.
Will the reader see the author as saying,
"Then a second person showed up so the crowd backed down."
and figure two women would have done this just as well. Or will the reader think,
"Then a man showed up to save the day."
.. if there are three attackers and he wins the fight on his own while she is unconscious, you need an explanation.
The best thing is probably to have him attack the mob first, then have others who were reluctant join the fight. That's realistic - people would hesitate to attack a mob all on their own - and gets you out of the Man saves Woman problem.
There's nothing wrong with either of these scenarios. But I don't think they address the OP's problem, in that the MMC is still 'saving' the FMC.
I think this is part of the large question -- does the author routinely treat the FMC as inherently lesser and weaker than the MMC? Writing, we choose scenes that showcase each protag's particular strengths.
If the MMC slings the unconscious female over his shoulder and escapes the crocodiles ... in a companion scene the FMC grabs a spear and prods the pack of hyenas away from the unconscious MMC.
Since we're writing for female readers mostly, we remember they will not enjoy a book where power, strength, competence and agency are overwhelming assigned to male characters. They will not like a succession of scenes where the balance of power rests solely in the male court.
Thus the tricky part of damsel-in-distress scenarios.
There are lots of kinds of strength.
Myself, I like the courage and power that does not lie in karate or carrying a gun. The pacifist in the front line of the protest who goes down under the boots of the police, the Texas woman keeping the farm going till her husband gets back from war, the fifteen-year-old raising her brothers and sisters because Momma went to heaven -- these are strong women and none of them would be worth damnspit in a riot.
..she chooses the hero who saves her.
As to falling in love with someone who claims to have rescued you but didn't ...
I don't think one should fall in love from gratitude and obligation.
One might fall in love with what seems to be courage and strength and self-sacrifice. Pity if it later turns out to be all lies.