If people who left and came back had a history of leaving again, I would agree that it isn't a wise move to let them come back. I can only go by my own personal experiences - long-time employees who leave and in a short time want to come back have not left a second time. A lot of replies said it's inevitable that she will just be leaving again, and perhaps that will happen sometime, but it hasn't happened before, and there's no reason to assume that's the case.
I have worked in sweatshops and I have worked in good companies. Some people have never worked anywhere else, and sometimes they get the idea that because it's not perfect, somewhere else is going to be better. And sometimes that other place is not very good at all. Looks good from the outside, they talk a good game, but once you join the team you see it was better where you used to be. If they realize they had a good thing at a good company and will be a very motivated employee in the future if they are rehired, that doesn't seem like a bad thing to me.
I once had a person at his 1 year anniversary review say right at the start of the meeting, "Look, before you even get started, if I'm not going to get a 25% raise, I'm quitting." I explained that his expectations were rather inflated - 25% raises after 1 year for someone right out of college just do not happen. He didn't care, didn't believe what I was saying, and quit. A year later he wanted to come back, but I passed. That's a person who won't be happy. The subject of this thread was happy, we were happy, and was sold a bill of goods to go to another place. It happens.
If the answer should have been "no, you can't come back" because she wanted a do-over, I'm not really following that logic. She did not assume she had a pass to come back. Nobody ever says that when someone leaves a job. No promises were made or implied.
Saying someone who left can never, ever come back is sometimes going to put you in a position where you have a job opening, and you're willing to consider everyone on earth except the one most qualified person, because that person once worked there. That wasn't the case this time since the job was filled, but a blanket rule saying people have one and only one chance to work at a company isn't really a good idea IMHO.