AN INSTRUCTOR PLT IN A PA28 RPTS A NEAR COLLISION WITH AN INSTRUCTOR AND STUDENT IN A DA20 KATANA ON RWY 13 AT PVU.

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WE WERE COMING BACK FROM AN INST TRAINING FLT IN MY STUDENT'S PERSONAL; PVTLY OWNED CHEROKEE. UPON LNDG; WE WERE UNABLE TO MAKE THE MIDFIELD TXWY. WE WERE ON RWY 13. I ANNOUNCED THAT WE WOULD BACK TAXI. SINCE WE WERE APPROX 250 FT PAST THE TXWY; IT WOULD BE EASIER TO TAXI BACK INSTEAD OF CONTINUING DOWN THE REMAINING 3000 FT OF RWY. I CALLED THAT WE WERE BACK TAXIING OVER THE CTAF AS MY STUDENT BEGAN TO MAKE THE 180 DEG TURN ON THE RWY. AS WE CAME AROUND; AN AIRPLANE (DIAMOND KATANA) WAS DSNDING OVER THE RWY AND COMING AT US. THEY CONTINUED THE DSCNT AND BEGAN A FLARE. THEY HELD THE AIRPLANE OFF THE GND ABOUT 2 FT. WE STARTED TO TAXI ONTO THE R-HAND SIDE OF THE RWY. THEY CONTINUED TO HOLD THE ACFT JUST OFF THE RWY AND THEN INITIATED A GAR. THE GAR CONSISTED OF HOLDING THE ACFT ABOUT 5 FT OFF OF THE RWY CTRLINE. WE TAXIED ALMOST ONTO THE DIRT AND GRASS ADJACENT TO THE RWY TO AVOID COLLISION. AS THE KATANA FLEW PAST; IT WAS LOW AND CLOSE ENOUGH TO OUR ACFT THAT WE COULD SEE THE STUDENT AND INSTRUCTOR INSIDE THE AIRPLANE. UPON QUESTIONING THE INSTRUCTOR OF THAT ACFT LATER; HE ADMITTED TO FLYING HIS ACFT LOW OVER THE RWY. HE STATED THAT EVEN THOUGH HE SAW US ON THE RWY; THAT HE SAW THAT THERE WAS AMPLE ROOM TO DEMONSTRATE A LNDG AND FLARE TO HIS STUDENT; BEFORE GAR.