This is the key point to me... she made a promise... set aside whether papers were signed, legal recourse, the job market, etc. ... she made a promise.
Absent material misrepresentation on the part of the employer, she failed to do her due diligence and rushed into a decision she now regrets... but she made a promise. Sure the employer cannot legally require her to keep her word, but it should not have to... character is driven internally, not by employment law externalities.
In today's world there is little loyalty either way between employers and employees, but a man (or woman's) word has to mean something does it not? She made a deal, she made a promise... she should honor her word.
I find in most of these cases the situation is not "tricky" the correct course is usually patently obvious... it is just hard, or not what one wants to do, and folks are seeking "permission" or "confirmation" from strangers to take a path they know is wrong...
I am not criticizing anyone's choices, I am not their priest or their father... but you asked for input, so there it is...