2 CREWS RPTED THAT 1 ACFT WAS CLRED FOR TKOF ON RWY 28L AT SFO SIMULTANEOUSLY WITH THE OTHER ACFT'S BEING CLRED TO CROSS RWY 28L.

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AFTER FO LANDED AT SFO RWY 28R; TWR INSTRUCTIONS WERE TO TURN L OFF RWY 28R AT TXWY E AND HOLD SHORT OF RWY 28L. CAPT; AS PNF; READ BACK THE CLRNC TO TURN L AT TXWY E AND HOLD SHORT OF RWY 28L. FO AND CAPT EXCHANGED CTL OF THE ACFT WHILE ON RWY 28R AFTER SLOWING AND CAPT BROUGHT ACFT TO STOP ON TXWY E. THERE WERE 2 TKOFS ON RWY 28L WHILE ACFT HELD SHORT OF RWY 28L. AFTER SECOND TKOF; TWR CLRED OUR ACFT TO 'CROSS RWY 28L AND CONTACT GND CTL ON 121.8.' FO READ BACK XING CLRNC; AND CAPT APPLIED PWR AND CROSSED RWY 28L. HALFWAY ACROSS RWY 28L TWR TOLD ACFT HOLDING IN POS FOR TKOF ON RWY 28L TO CANCEL TKOF CLRNC. AT THAT TIME; CAPT NOTICED ACFT IN HOLDING POS HAD TKOF LIGHTS ON; BUT NEITHER HE NOR FO EVER HEARD A TKOF CLRNC FOR ACFT IN POS. UPON ARR AT GATE; CAPT CALLED TWR SUPVR TO REEMPHASIZE THAT HE HAD BEEN CLRED TO CROSS RWY 28L; AND THE CLRNC HAD BEEN READ BACK. TWR SUPVR INDICATED THAT HE THOUGHT THAT WAS THE CASE AND THAT HE WOULD LISTEN TO THE TAPES TO VERIFY. CAPT INDICATED THAT HAD HE HEARD A TKOF CLRNC FOR THE ACFT IN POS; HE NEVER WOULD HAVE ACCEPTED THE CLRNC TO CROSS RWY 28L. TWR SUPVR CONCURRED. SUPPLEMENTAL INFO FROM ACN 466862: WE WERE CLRED FOR TKOF RWY 28L. AFTER COMPLETING THE TKOF CHKLIST; SETTING TKOF PWR; CHKING HEADINGS AND XCHKING INSTS; I SAW THE AIRSPD COME ALIVE AND BEGAN TO SHIFT MY SCAN OUTSIDE AND DOWN THE RWY. AT THAT MOMENT I SAW AN AIR TRANSPORT ACFT XING OUR RWY. AS I BEGAN AN ABORT; WE HEARD THE TWR SAY ABORT. SUCCESSFUL ABORT AT APPROX 60-80 KTS. EXITED RWY; CONSULTED RED BOOK FOR ABORT PROC AND BRAKE LIMITS. EVERYTHING WELL WITHIN LIMITS SO WE GOT IN LINE AND DEPARTED APPROX 10 MINS LATER. REMAINDER UNEVENTFUL. UPON TALKING WITH SFO TWR CHIEF LATER; HE TOLD US THE CTLR WAS A TRAINEE AND HAD IN FACT CLRED US FOR TKOF AND HAD CLRED THE OTHER ACFT TO CROSS OUR RWY. THIS INFO CAME OFF THE TWR TAPES.