Shortly before interviewing a teacher for a post, we learned that she had already been offered and had accepted in writing a post at another school. While admitting what happened, she is now protesting that we acted improperly in withdrawing the invitation to interview. Did we?
By accepting the offer of the post in the first school this teacher had entered into a contractual obligation which would have been broken had she subsequently decided to come to you. This sort of thing happens now and again, although it is probably not worth the trouble of suing for breach of contract. It is always tempting to go for the better job, but it should be discouraged. The honourable course is to ask the first school to allow a few days before requiring confirmation. If it will not, then one has to make up one's mind, one way or the other.
You were certainly well within your rights to withdraw the invitation to interview. Quite apart from your criteria for selection, you might argue that it was a basic requirement of anyone you employ to be trustworthy and capable of keeping their word. The action of this teacher is more than sufficient to raise doubts in your mind in this respect.