It might help to put things in chronological order.

First, Mary and I meet.

Second, Mary and I get acquainted.

Third, Mary and I are acquainted.

These three things are not the same. "Meet" is the first step in the process (introductions, etc.). Next comes "getting acquainted" which means learning a few things about each other, seeing if you enjoy each others company etc. If that's successful, then you "are acquainted" with each other, meaning that you've already completed the first two steps.