There are a lot of people commenting that she didn't actually resign. I agree, but it sounds like the conversation went like this:

employee: I'm not happy about x, y and z. If you don't do those, I'm going to quit.

manager: well we are not going to do those, so thank you for your time. We accept your resignation and would like it to start immediately (i.e. you're fired).

If you are gonna tell your manager that you plan to resign if a condition isn't met, then what do you expect them to say if they don't plan to fulfill that condition? It sounds like she was expecting them to say "Hey, well we don't want to meet your demands, but sure, we're happy to have a disgruntled employee around here, so feel free to stick around, or you could just quit on your own timeline, no sweat".

I suspect that many people would be fired on the spot for threatening to resign, so don't threaten it if you aren't okay with that consequence.