AN ATX FLC MISINTERPRETS THEIR CLRNC WHEN IT IS GARBLED AND SIMPLY 'ROGERS' THE CTLR'S RESPONSE AND PROCEEDS ON THE REQUESTED DIRECT CLRNC TO UJM; AR.

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WHILE FLYING FROM DAL TO MEM DEP; LEFT US ON A VECTOR TO JOIN THE DEP PROC. (DAL5 ELD TRANSITION UJM MEM). WE JOINED THE OUTBOUND 084 DEG RADIAL OFF OF THE MAVERICK (TTT) VOR AND CONTINUED OUR CLB TO 17000 FT. WE WERE THEN HANDED OFF TO ZFW AND CLRED UP TO FL330. DURING THE CLB WE REQUESTED A SHORT CUT DIRECT TO UJM FOR THE MARVELLE THREE ARR INTO MEM. THE CTR CTLR STATED 'UNABLE AT THIS TIME.' THE TROUBLE IS; HE WAS HARD TO UNDERSTAND PLUS IT WAS A POOR XMISSION AND SLIGHTLY GARBLED. WE HEARD IT AS 'CLRED AS REQUESTED.' MY COPLT AND I HAD A BRIEF DISCUSSION AS TO WHAT WAS SAID AND WE BOTH AGREED WE WERE CLRED AS REQUESTED. A BIG PART OF THE PROB WAS I READ BACK ONLY OUR CALL SIGN. ATC ASSUMING WE HAD 'GOTTEN THE MESSAGE;' DID NOT CHALLENGE US. SO WE THEN PROCEEDED DIRECT TO UJM. AFTER SOME TIME 5-8 MINS; ATC RADIOED TO US WONDERING WHERE WE WERE GOING. WE TOLD HIM DIRECT UJM. HE THEN LET US KNOW WE WERE NOT CLRED THAT WAY. THIS COULD HAVE BEEN AVOIDED IF I HAD GIVEN A FULL READBACK OF OUR CLRNC. THEN ATC WOULD HAVE BEEN GIVEN THE OPPORTUNITY TO CHALLENGE US AND CORRECT THE SIT.