PA28 ON BASE TO TWF RWY 25 EXPERIENCED CONFLICT WITH STRAIGHT IN TFC; ATC'S SPACING/SEQUENCING JUDGEMENT LISTED AS CONTRIBUTORY.

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AS WE WERE RETURNING TO TWF FROM THE SW AFTER A TRAINING FLT; ANOTHER CHEROKEE RPTED SEVERAL MI N. THE LCL CTLR INSTRUCTED MY STUDENT TO RPT ON A L DOWNWIND FOR RWY 25. THE OTHER CHEROKEE WAS INSTRUCTED TO RPT 2 MI N. MY STUDENT RPTED L DOWNWIND AND INITIATED THE LNDG SEQUENCE. AS WE TURNED BASE I LOOKED FOR THE OTHER CHEROKEE; BUT DID NOT SEE IT. I WASN'T WORRIED BECAUSE I HAD NOT HEARD HIM RPT 2 MI OUT; SO I ASSUMED THAT HE WAS STILL MORE THAN 2 MI FROM THE ARPT. THE CHEROKEE THEN RPTED 2 MI OUT AND HE WAS TOLD THAT HE WAS '#2 BEHIND A CHEROKEE TURNING FROM DOWNWIND TO L BASE.' HE ACKNOWLEDGED. AS MY STUDENT STARTING MAKING HIS TURN FROM BASE TO FINAL THE CTLR TOLD THE OTHER CHEROKEE 'YOU ARE AHEAD OF THE OTHER CHEROKEE; YOU ARE CLRED TO LAND; ACFT X YOU ARE NOW #2.' I TOLD THE TWR THAT WE DID NOT HAVE THE OTHER PLANE IN SIGHT. MY STUDENT WAS NOW IN HIS TURN TO FINAL AND I SAW THE OTHER PLANE TO OUR R -- FURTHER FROM THE ARPT; AND SLIGHTLY BELOW US. I TOOK CTL OF THE PLANE; INITIATED A L CLBING TURN TO AVOID A COLLISION. THE CTLR THEN INSTRUCTED US TO CONTINUE OUR TURN AND FOLLOW THE OTHER CHEROKEE. WHEN THINGS CALMED DOWN THE CTLR EXPLAINED THAT HE HAD MISJUDGED OUR DISTANCE BECAUSE OF OUR CRAB ANGLE AND THOUGHT WE WERE FURTHER OUT THAN WE WERE. HAD WE NOT STARTED THE CLBING TURN WHEN WE DID THE OTHER PLANE WOULD HAVE BEEN WITHIN A VERY FEW FEET OF US WHEN WE COMPLETED THE TURN; OR POSSIBLY HAVE COLLIDED WITH US. I BELIEVE THERE WERE 2 FACTORS IN THIS NEAR MISS. THE OTHER CHEROKEE SEEMS TO HAVE BEEN MUCH CLOSER THAN 2 MI WHEN HE RPTED. THE LCL CTLR GROSSLY MISJUDGED OUR DISTANCE FROM THE FIELD.