PLT OF SMA BACK TAXIING ON UNCTLED ARPT RWY WAS ALMOST HIT BY ANOTHER SMA MAKING A GAR.

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SMALL HIGH-WING ACFT (PROBABLY C-150) INCORRECTLY ENTERED THE TFC PATTERN CREATING A HAZARD FOR ANOTHER ACFT ALREADY ON FINAL TO RWY 27. WE WERE IN POS TO BACK-TAXI FOR TKOF AFTER MAKING A PLT CHANGE. WE WAITED FOR SUFFICIENT SPACE (NO ACFT ON FINAL) TO BEGIN OUR BACK- TAXI. CESSNA ACFT FLEW WHAT APPEARED TO BE A VERY TIGHT BASE AND FINAL SUCH THAT WE WERE STILL MIDFIELD ON OUR BACK-TAXI AS HE TURNED FINAL. I COMMENTED TO MY STUDENT THAT THE ACFT HAD BETTER BE INTENDING TO GAR. OTHER ACFT IN PATTERN THAT HAD BEEN PREVIOUSLY CUT OFF BY CESSNA ASKED IF THERE WAS SOMEONE BACK-TAXIING SO THAT THE CESSNA MIGHT BECOME AWARE THAT WE WERE STILL ON THE RWY. AS THE CESSNA BEGAN TO FLARE APPROX 100 YARDS AHEAD OF US IT WAS CLR THAT HE DID NOT SEE US. WE BEGAN TO SLOW AND VEER TO THE R TO AVOID HIS PATH. HE THEN SAW US AND BEGAN A GAR (TERM USED LOOSELY). HIS GAR APPEARED TO BE IN AN ALMOST STALLED CONDITION GIVEN THE ATTITUDE AND ROCKING OF HIS WINGS (OTHER ACFT IN THE PATTERN VERIFIED MY OBSERVATION AND AGREED WITH MY ANALYSIS. AT THE POINT WHEN THE CESSNA CLRED US I ESTIMATE 25 FT VERT SEPARATION; ZERO HORIZ SEPARATION. OUR ACFT HAD MADE ALL AIM RECOMMENDED RADIO CALLS THROUGHOUT THE DURATION OF OUR STAY AT RANTOUL. THE CESSNA DEPARTED UPWIND; WE DID NOT SEE HIM AGAIN. IN REVIEWING THE ABOVE INCIDENT IT SHOULD BE NOTED THAT MERE FOLLOWING OF AIM PROCS DOES NOT KEEP EVERYONE SAFE. A CONSTANT VIGILANCE FOR THOSE WHO ARE NOT FOLLOWING PROCS MUST BE KEPT. IN ADDITION; IT SHOULD BE POINTED OUT THAT WHEN ONE IS UNCERTAIN ABOUT THE ACTIONS OF ANOTHER PLT/ACFT; IT IS BEST NOT TO SECOND GUESS THEIR INTENTIONS. WAIT UNTIL ONE IS ASSURED OF ADEQUATE CLRNC THROUGHOUT A MANEUVER; NOT JUST WHEN STARTING THE MANEUVER.