PLT DEVIATED FROM ASSIGNED ALT AFTER BEING CLRED FOR THE 'TRANSITION' DURING A STUDENT TRAINING FLT.

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MY INST STUDENT AND I WERE ON RECENT IFR XCOUNTRY TRAINING FLT TO FULFILL REQUIREMENTS FOR HIS INST RATING. WE WANTED TO SHOOT NDB-10 APCH TO CGI DUE LOC OTS; REQUESTED 'ZKC' FOR SAME VIA TRANSITION FROM FAM VOR. CTR ANTENNA LOCATION MUST BE POOR AS RECEPTION OF CTR WAS GARBLED AND ALMOST TOTALLY UNREADABLE; WHICH WAS PASSED ON TO CTR AS SUCH. WE FINALLY UNDERSTOOD CTR TO SAY 'OK TO FLY FAM TRANSITION AND EXPECT NDB-10 APCH CLRNC.' THE PUBLISHED TRANSITION CALLS FOR 3000 FT ALT WE WERE AT 5000 AND COMMENCED DSCNT TO 3000. AT 4000 FT CTR SAID HE 'OKAYED YOU TO FLY TRANSITION BUT MAINTAIN 5000 FT.' WE MAY HAVE MISSED THIS DUE TO LOUSY RECEPTION; BUT IF NOT; DSCNT TO 3000 FT WOULD HAVE BEEN OK AS INSTRUCTION TO 'FLY TRANSITION' WOULD TO ME MEAN TO FLY IT AS PUBLISHED. NO CONFLICT RESULTED AND WE WERE ALLOWED TO STAY AT 4000 FT. ALSO MY STUDENT HAD FILED FLT PLAN UNDER HIS NAME IN ERROR; INSTEAD OF MY NAME. (HE IS NOT YET INST RATED). CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: ADVISED RPTR THAT CLRED FOR THE 'TRANSITION' DOES NOT MEAN CLRNC TO A LOWER ALT. THE ALT SHOWN IN THIS INSTANCE WAS AVAILABLE ONLY WHEN NOT MAKING A PROC TURN.