RWY INCURSION. ACR X UNAUTH RWY ENTRY.

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ORD GND ADVISED; ACR X TO TAXI TO RWY 32L FOR DEP FROM T- 10 INTXN. AS FLT APCHED DEP POS; GND CTL THAT GAVE US OUR TAXI CLRNC; ADVISED US TO MONITOR TWR FREQ; THEY WOULD CALL US FOR DEP CLRNC. TWR FREQ WAS SELECTED AND THE TWR CLRED US INTO POS TO HOLD. ALL INSTRUCTIONS WERE READ BACK IN FULL. AFTER BEING IN POS AND HOLDING FOR APPROX 20 SECONDS WITHOUT ANY COMS ON THE FREQ; I REQUESTED A RADIO CHK BY XMITTING; ORD TWR ACR X REQUEST RADIO CHK. THE CTLR INDICATED THAT WE WERE ON DEP CTL AND REQUESTED OUR POS. I ADVISED OF OUR POS AND ASKED IF THIS WAS ORD TWR. THE CTLR ASKED IF WE WERE TOLD TO CONTACT TWR. I REPLIED; YES WE WERE; YOU GAVE US CLRNC INTO POS TO HOLD RWY 32L AT INTXN T-10 AND I READ THE CLRNC BACK TO YOU. THE CTLR GAVE US A NEW FREQ AND TOLD US TO CONTACT ORD TWR IMMEDIATELY. WE DID SO. THE 'NEW' TWR FREQ CTLR ASKED IF WE WERE HAVING RADIO TROUBLE. I RESPONDED NO; AND THAT THE GND CTLR HAD GIVEN US TO TWR; AND TWR HAD CLRED US INTO POS. THIS 'NEW' TWR CTLR CLRED US FOR TKOF AND NO FURTHER PROBS DEVELOPED. AFTER ARRIVING AT DEST ARPT; I CALLED ORD TWR TO DISCUSS THE FREQ PROB. THE CTLR'S EXPLANATION OF HOW WE WERE CLRED ONTO THE RWY BY TWR/DEP WAS UNCLR. THE CTLR SAID THERE WAS NO CONFLICT AND THAT THIS TYPE OF SIT EVOLVED DAILY AT ORD ON MULTIPLE OCCASIONS.