C172 EXPERIENCES NMAC WITH ANOTHER CESSNA IN THE TRAFFIC PATTERN. INCORRECT IDENTIFICATION BY TOWER MAY HAVE CONTRIBUTED.

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I WAS PILOTING A C172SP EQUIPPED WITH A G1000 COCKPIT ON AN INSTRUCTIONAL FLT WITH MY FLT INSTRUCTOR. WE HAD JUST CONTACTED THE TWR AT ZZZ AND ADVISED OUR POS AS NE OF THE ARMY AIRBASE AND DIRECTLY OVER ABC. THE TWR REPLIED WITH INSTRUCTIONS FOR A L TFC APCH FOR RWY XX AND ALSO ADVISED OF TFC IN OUR VICINITY. OUR ALT AT THIS POINT WAS 1180 FT MSL; AND THE TFC INFO FROM TWR WAS FOR A CESSNA 2 MI OUT AT 1600 FT MSL. AT THIS TIME OUR C172 WAS DOWNWIND FOR L TFC ON RWY XX. MY INSTRUCTOR AND I WERE BOTH LOOKING FOR THE TFC WHEN I HEARD THE G1000 (TCAS) SAY: 'TFC.' I IMMEDIATELY LOOKED TO OUR 12 O'CLOCK POS AND SAW A C172/182 TRACKING A HEAD-ON COURSE TO OUR ACFT AT 100-150 FT ABOVE US. I IMMEDIATELY ASSESSED WHETHER EVASIVE ACTION WAS NECESSARY AND DETERMINED (ALONG WITH MY INSTRUCTOR) THAT NO ACTION WAS NECESSARY. DURING OUR DEBRIEF MY INSTRUCTOR AND I DISCUSSED WHAT COULD HAVE LED TO THIS NEAR MISS. SEVERAL FACTORS WERE AT HAND: FIRST; THE TWR CTLR LOST TRACK OF THE 2 ACFT AT NEAR IDENTICAL ALTS ON OPPOSING; HEAD-ON COURSES. SECOND; THE TWR CTLR CALLED THE TFC BEFORE REALIZING OUR ENTRY INTO THE DOWNWIND LEG OF THE PATTERN WOULD CAUSE A CONFLICT. THIRD AND FINALLY; THE OPPOSING ACFT SHOULD NOT HAVE BEEN SO LOW ON A COURSE NEAR THE DOWNWIND LEG OF ZZZ'S TFC PATTERN (SHE SHOULD HAVE BEEN AT LEAST 500 FT ABOVE PATTERN ALT). BECAUSE OF OUR CLOSURE RATE; THE '2 MI' SEPARATION DISAPPEARED WITHIN A MATTER OF SECONDS.