A counter offer, once tendered, cancels the original offer.

Legally speaking, a counter offer, once tendered, cancels the original offer. Therefore, LZ no longer had an offer the moment she counter-offered. As such, to say that the employer rescinded the original offer is technically incorrect. Rather, the situation really is: LZ rejected the employer's original offer by tendering a counter offer, which was, in turn, rejected by the employer.

Sorry for being technical, but thought it might help clear up some common misunderstanding.