B737 FLT CREW DURING TAXI HAS A RWY INCURSION AT PHL.

Narrative

WE CALLED GND CTL AND UNDERSTOOD WE WERE CLRED TO CROSS RWY 27R; TXWY N; TO RWY 27L AND THIS IS WHAT THE FO READ BACK. NO RESPONSE FROM GND SO WE CROSSED RWY 27R; NOTICED AN ACFT IN POS FOR TKOF BUT NO CALLS OR CORRECTION FROM GND. APPARENTLY; THE GND CTLR WANTED US TO TURN L ON TXWY K AND TAXI FOR TKOF TO RWY 27R. WHEN WE REALIZED THERE HAD BEEN A MISCOM WE ADVISED THE GND CTLR WE HAD TAXIED AS WE READ BACK AND AFTER SOME CHKING HE ADVISED HE HAD MISSED READBACK AND AS TO OUR QUESTION OF DO WE NEED TO WRITE A RPT; HE SAID 'NO HARM; NO FOUL.' THIS STILL COULD HAVE BEEN A MORE SERIOUS INCIDENT AND IT REMINDS ME TO 'SLOW DOWN' AND ENSURE BY ALL MEANS POSSIBLE THAT WHAT I HEARD WAS WHAT WAS SAID AND MEANT. SUPPLEMENTAL INFO FROM ACN 689050: CONTACTED GND CTL ON SPOT 8. I AM NOT SURE WHAT HE REALLY SAID; BUT WHAT I HEARD AND WHAT I READ BACK WAS 'TXWY K; TXWY N; CROSS THE R SIDE AND CONTACT TWR.' AFTER XING RWY 27R; WE WERE INFORMED THAT WE WERE NOT CLRED TO CROSS RWY 27R BECAUSE THAT WAS THE DEP RWY.