Actually the Theorem states, that you must sample with a rate strictly GREATER THAN (not equal) than twice the highest frequency. Exactly because sampling only the zero crossings is not enough.

Ofcourse depending on how exactly you want to process your samples it might be convenient to have an even higher sampling rate. And if you know your signal does not contain low frequencies (=not using the full bandwidth) you might get away with even lower sampling rates.

But the general case is: you must sample with a rate strictly greater than twice the highest frequences.