My choice of which to believe is based on the fact that the article presents some evidence that the first scenario is true:
1. The hire actually gave the reason as not feeling comfortable with her competence. 2. She claims to have been feeling unhappy with her own performance for a while and on shaky ground at the company. 3. The rest of the team accepted her suggestion and reasoning that it was her and that someone else should try to get the guy back.
The only evidence presented for the second scenario is the guess that her coach makes.
Given that, I don't think we are in a situation where we should bias in favour of innocent until proven guilty. We can just make our own best guess based on what we know.
Your evidence 2 and 3 are weak. Being in a high pressure job often means being in a position where you (and the company) can't afford a big disaster. Lots of people are hard on themselves, it doesn't mean she was on shaky ground because of her competence (her colleagues wanted her around for another year at least). She insisted on leaving to make this guy happy because his stated reason for rejecting the job was her. Her colleagues wanted the guy to join them and they didn't have any reason to refuse her resignation. That doesn't shed any light on why the man was unhappy with her in the first place.
The guy didn't give convincing examples or well thought out reasons, he seems to have just made a guess that she was incompetent. You think his guess is unbiased and the coach and the author's guesses are biased. Even though it is the coach's job to make objective judgements about these things. In this scenario the man, the author and the coach all make judgements given information we are not privy to. Each of them has their own biases, their own agendas. I think the man's inability to explain his dislike when pressed, and the fact that the coach is supposed to provide negative criticism indicates that the coach's judgement is most likely correct.
The story does not strongly point to the problem being her not her gender. The guy in question did something extraordinary (pulling out of an accepted job offer) without being able to give much justification besides vaguely disliking her. If she was incompetent or had a poor personal manner then that is exactly something you would expect the man in question, her colleagues and her coach to bring up.
You can interpret this story in two ways:
a) The man had a non-sexist reason for disliking the author so much he backed out of an accepted job offer, but he was unable or unwilling to express that reason specifically, even though he was willing to tell her that she was the problem. The author is incompetent or unlikable, her colleagues are too incompetent to notice or say anything and the author's coach is so incompetent that she just spouts feminist paranoia instead of actually being helpful.
b) The author, the coach and the author's colleagues are all reasonably professional and competent, the man in question is from a culture where older men don't tend to like being under the authority of young women and this made him increasingly uncomfortable over time. He backed out of the job because of this feeling of discomfort, but was unwilling to give that as his reason because he knew it would be seen as unprofessional.
I believe that your choice of which of these to believe indicates that YOU are sexist.