You cannot make those kinds of threats if you aren't prepared to follow through.
If they were really 'forced' to accept her resignation, what harm would informing her that they couldn't meet her demands do? It seems painfully obvious to me they didn't want to risk working it out and just used this as an opportunity to get rid of her.
>We accept your resignation with immediate effect.
That couldn't be clearer to me. Negotiation is bad in those cases because they'll always resent you (and such demands are only made when emotions are at boiling point).
I've literally never given ultimatums to any employer, because that's like negotiating with a nuclear weapon equipped.
This is the best strategy in most other relationships too. You must always leave room for reconciliation and/or compromise. Unless you really would like the relationship to be over.
In any case, it seems there's more than meets the eye here. Her team INCLUDING her manager appear to be standing by her and they would likely know the details better than any of us.
I wouldn't be so quick to jump to conclusions.