AN APPARENT READBACK AND OR HEARBACK ERROR RESULTED IN A C750 FLT CREW TO CLB TO A WRONG ALT.

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DURING CLBOUT FROM GSO; NUMEROUS INCREMENTAL CLB CLRNCS WERE RECEIVED. ONE SUCH CLRNC WAS UNDERSTOOD BY BOTH MYSELF (THE PNF) AND THE PF TO BE 'CLB AND MAINTAIN FL290.' THE READBACK WAS 'ROGER; FL290; (CALL SIGN).' FL290 WAS SET IN THE ALT ALERTING DEVICE; AND CLB WAS INITIATED. DURING THIS PERIOD; A HDOF WAS ACCOMPLISHED TO ANOTHER ARTCC SECTOR. APCHING LEVELOFF AT FL290; A TA WAS RECEIVED AND A TARGET WAS OBSERVED AT 10 O'CLOCK POS; SLIGHTLY HIGHER; OPPOSITE DIRECTION; WITH A LATERAL SEPARATION OF 4.5 MI. SHORTLY THEREAFTER; THE CTLR QUERIED US AS TO OUR ALT. UPON OUR REPLY; HE STATED HE BELIEVED THE PRIOR CTLR 'WANTED US AT FL280.' WE CONFIRMED WITHIN THE COCKPIT THAT WE HAD HEARD AND READ BACK FL290; THEN RELAYED THIS INFO TO THE CTLR. HE SEEMED UNCONCERNED; AND SIMPLY ASSIGNED US A HIGHER ALT TO CONTINUE OUR CLB. BASED UPON THE TFC CONFLICT; IT SEEMS LIKELY THE PRIOR CTLR WANTED US AT FL280. IF SO; EITHER HE VERBALLY ASSIGNED FL290 IN ERROR OR WE HEARD; AND READ BACK; FL290 IN ERROR. IN EITHER CASE; THE CTLR FAILED TO CATCH; AND CORRECT; THE ERROR UPON READBACK.