AN ACR TWIN JET FOLLOWS AN RJ ACROSS RWY 27L WHEN THEIR INITIAL CLRNC HAD BEEN TO 'HOLD SHORT OF RWY 27L; FOLLOW THE RJ.'

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WE RECEIVED TAXI CLRNC TO TAXI TO RWY 27L VIA TXWY T; HOLD SHORT OF RWY 27L AND FOLLOW THE 'RJ.' WHILE I WAS UPDATING THE FMC; THE ACFT IN FRONT OF THE RJ VERIFIED THAT THEY WERE CLRED TO CROSS THE RWY. THE ACFT CONTINUED AND THE RJ FOLLOWED THE FIRST ACFT. I INFORMED THE CAPT THAT I WAS ONCE AGAIN 'HEADS UP' AND ASKED IF WE WERE CLRED TO CROSS RWY 27L. HE INFORMED ME THAT WE WERE CLRED TO CROSS. I INFORMED HIM I DID NOT HEAR THE CLRNC DUE TO PERFORMING OTHER DUTIES. HE ONCE AGAIN INFORMED ME THAT WE WERE TO FOLLOW THE RJ AND THAT HE WAS CLRED TO CROSS THE RWY. WE CLRED THE RWY AND PROCEEDED TO CROSS. UPON REACHING THE OTHER SIDE OF THE RWY; WE WERE INFORMED THAT WE IN FACT DID NOT HAVE CLRNC TO CROSS RWY 27L. WE APOLOGIZED DUE TO FREQ CONGESTION. WE WERE UNABLE TO ASK FOR CLARIFICATION. IF GIVING INSTRUCTIONS TO FOLLOW ACFT AROUND SHOULD ADVISE EACH ACFT INDIVIDUALLY. INSTRUCTIONS TO FOLLOW OR CROSS INTXNS. SUPPLEMENTAL INFO FROM ACN 476307: GND CTL VERY BUSY WITH DELAYS OUTBOUND DUE TO WX. OUR CLRNC WAS TO RWY 27L; FOLLOW THE' RJ.' WE WERE THEN TOLD TO MONITOR TWR FREQ. A COMBINATION OF 'PERCEIVED' TAXI CLRNC; OTHER COMS; A CLR RWY ALL LED TO THIS XING WITHOUT CLRNC. IN A 'PERFECT' WORLD; EACH ACFT SHOULD RECEIVE ITS OWN CLRNC. THE SAME CONGESTION ON FREQ THAT LED THE CTLR TO GIVE THE 'FOLLOW' CLRNC ALSO LED US TO CROSS WITHOUT VERIFYING. IN THE FUTURE; I WILL ALWAYS VERIFY CLRNC TO CROSS A RWY.