That is a very unwise way to look at evidence. You can't apply the legal standard of evidence to the rest of the world, because courtrooms have facilities that make evidence highly available. You have discovery, expert analysis, compelled testimony, and the possibility of sealing records to protect the parties involved. When evidence should be available, absence of evidence is strong evidence of absence.
Outside of court, things work differently. But we have other ways of dealing with evidence and trust, which wouldn't work very well in the courtroom.
But you already know this, and I can prove it. Suppose a close friend, who you trust, tells you that someone broke into his house and stole his TV. Are you going to set aside judgment about this situation until you can collect more evidence? Are you going to demand that he show you security camera footage? Probably not, and rightly so.
You believe your friend because of reputation. Your friend has staked your trust in him against his lying. You both know that if you find out that he lied, it will hurt your friendship, and you will be unlikely to trust him in the future. This is very much like the concept of precommitment in game theory. He has set up the situation so that if his claims turn out to be false, he's likely to suffer negative consequences. This allows him to produce evidence seemingly out of thin air, by tying his personal interests to the veracity of his claim.
Now look at the two parties in this case. Fowler has staked her professional reputation on the truth of her allegations. She posted this under her real name, on her blog which is the second Google result for her name. If she turns out to be lying, things will go very badly for her. Not only will it be difficult for her to find a company willing to hire her, but Uber could sue her for defamation.
Uber has staked... nothing. Indeed, they've done the opposite. Rather than cutting off their escape routes to establish credibility, they sacrificed credibility to buy an escape route. They publicly stated that their CEO is too unaware of the goings on at his own company to confirm or deny the allegations. They took a hit now so that they have more flexibility later.
It would be hard to overstate how bad this looks. There's no good outcome for the move Uber just made, which means that they're probably hedging against something even worse. Barring the possibility that Uber has no idea how to handle basic PR scenarios, the only reasonable explanation is that they know they're holding a weak hand.