B727 FLC TURNED FOR DIRECT FLT TO A VOR DURING DEP CLB AND WERE INFORMED BY ARTCC CTLR THAT THEY WERE GIVEN ONLY AN 'EXPECT DIRECT.' HOWEVER; THE CTLR HAD NOT HEARD THE CREW'S INCORRECT READBACK.

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WE WERE CLBING OUT OF NEW ORLEANS NBOUND ENRTE TO DFW. ON THE CLBOUT; CTLR GAVE US INSTRUCTIONS TO CLB TO A NEW ALT (I THINK FL230) AND I THOUGHT I HEARD HIM SAY 'EXPECT DIRECT AEX VOR;' BUT THE CAPT READ BACK 'UP TO FL230 AND DIRECT AEX.' THE CTLR DID NOT CORRECT HIM AND THE CONSENSUS IN THE COCKPIT WAS THAT HE CLRED US DIRECT. I DID NOT HEAR THE CTLR CLRLY ENOUGH TO QUESTION THE DIRECTION AND TURNED DIRECT AEX; AFTER VERIFYING THE INSTRUCTIONS WITH THE CAPT. I HAD NO REASON TO DOUBT -- COM AND PROFESSIONALISM ALONG WITH CREW WERE AT A HIGH LEVEL THROUGHOUT THE TRIP. INSPITE OF THAT; THE TURN DIRECT HAD NOT BEEN GIVEN BY THE CTLR. HE ASKED US OUR HDG; WE TOLD HIM; AND HE INFORMED US THAT HE HAD NOT ISSUED US THAT CLRNC. THE CAPT APOLOGIZED AND TOLD HIM HE READ BACK DIRECT AEX. AFTER A PAUSE; THE CTLR SAID THAT HE MISSED THE READBACK AND FOR US TO SWITCH FREQS TO THE NEXT CTLR. THERE WERE NO ACFT ON OUR TCASII OUT TO 50 NM SCOPE. THE CTLR DID NOT SAY OR IMPLY THAT HE INTENDED TO TAKE ACTION.