As a former employer, I have to say it is an utter turn-off when a potential candidate asks about pay early on in the process. It becomes readily clear that the candidate is more interested in "what's in it for me?" than in working at the company to help it grow and develop.
Did the company make a mistake in not offering a second interview? No, the mistake they made was in articulating the reasons for declining her. In these days of litigation and social media, employers are effectively muzzled with regard to commenting on employees or even prospective employees. They should have just said, "Thanks but no thanks" without explanation - none is owed - and moved on to the next candidate. They are not required to give reasons, and this lady's campaign to smear the company is a good reason why not.