B737 DEP FROM SAT IS QUESTIONED BY ATC REF TKOF CLRNC.

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JUST AFTER INITIATION OF TKOF ROLL ON RWY 3; SAT TWR DIRECTED US TO 'CANCEL TKOF CLRNC.' I MOMENTARILY REDUCED PWR SLIGHTLY; AFTER WHICH TWR TOLD US TO 'CONTINUE TKOF IF SAFE TO DO SO.' SINCE BOTH THE CAPT AND I WERE COMFORTABLE WITH CONTINUING THE TKOF; I RE-ADVANCED THE PWR TO TKOF THRUST AND MADE AN UNEVENTFUL TKOF. ONCE SAFELY AIRBORNE; TWR TOLD US HE 'THOUGHT HE CLRED US ON TO HOLD.' THE CLRNC I REMEMBER WAS 'COMPANY NUMBER; CLRED FOR TKOF; TFC DEPARTING XING RWY.' I ALSO BELIEVED I READ BACK; 'COMPANY NUMBER; CLRED FOR TKOF.' I REMEMBER THINKING THAT IT WAS ODD THAT TWR WOULD CLR US FOR TKOF WITH ANOTHER ACFT DEPARTING ON RWY 12R; BUT IF FIGURED TWR HAD THE SPACING WORKED OUT AND WAS JUST TRYING TO BE EFFICIENT. IN THE FUTURE; I WILL QUESTION A TKOF CLRNC LIKE THIS. NAME NUMBER 'PS.' WE FINALLY TALKED TO SAT TWR ON THE PHONE. ACCORDING TO THE TWR SUPVR; A REVIEW OF THE TAPES INDICATES THAT THEY DID CLR US FOR TKOF AND I DID READ BACK 'CLRED FOR TKOF.' THEY ARE TAKING UP THE ISSUE WITH THE CTLR. LESSON LEARNED FOR ME IS THAT IF I HAD QUESTIONED WHAT I THOUGHT WAS AN ODD TKOF CLRNC THIS WHOLE AFFAIR COULD HAVE BEEN AVOIDED. SUPPLEMENTAL INFO FROM ACN 590635: THE CONTRIBUTING FACTORS WERE THE USE OF MULTIPLE AND INTERSECTING RWYS. IN HINDSIGHT; WE COULD HAVE QUESTIONED THE CLRNC TO TAKE OFF WITH DEPARTING TFC ON THE INTERSECTING RWY. HOWEVER; THE OTHER ACFT ON RWY 12R WAS JUST BEGINNING HIS ROLL WHEN WE PASSED THE INTXN AND THE CONFLICT WAS NOT A FACTOR IN MY OPINION.