ACR X RWY INCURSION HAD LTSS FROM ACR Y ON TKOF ROLL. SYS ERROR.

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ACFT X MEETS THE SAME SPECS AS ACFT #1. WHILE TAXIING SBOUND ON W1 IN ACFT #1; WE HEARD DULLES GND CTLR ASK ACFT X IF THEY COULD ACCEPT AN INTXN DEP OFF RWY 1L AT TXWY W8. ACFT X WAS TAXIING DIRECTLY BEHIND ACFT #1 ON W1 WHEN THE REQUEST WAS MADE. FOR SOME REASON THE DULLES CTLRS WANTED ACFT X TO DEPART PRIOR TO ACFT #1. ACFT X REPLIED THAT THEY WOULD ACCEPT THE INTXN DEP. WE (ACFT) CONTINUED TO TAXI FULL LENGTH FOR RWY 1L AND STOPPED BEHIND ACFT Y; HOLDING SHORT OF RWY 1L AT R6. ACFT Y WAS TOLD BY DULLES TWR TO TAXI INTO POS AND HOLD ON RWY 1L AND THEN SUBSEQUENTLY CLRED FOR TKOF SHORTLY THEREAFTER. AS ACFT Y INITIATED ITS TKOF ROLL; ACFT X WAS TOLD TO TAXI INTO POS AND HOLD BY DULLES TWR. ACFT X MOVED FORWARD SLIGHTLY THEN STOPPED; QUERIED DULLES TWR IF THEY HAD JUST CLRED SOMEONE FOR TKOF ON RWY 1L. TWR REPLIED THAT THEY HAD CLRED ACFT Y FOR TKOF AND THAT THEY THOUGHT ACFT X WAS AWAITING TKOF AT FULL LENGTH RWY 1L. A COLLISION WAS AVOIDED DUE TO THE VIGILANCE AND SITUATIONAL AWARENESS OF THE CREW IN ACFT X. REDUCED VISIBILITY COULD HAVE AGGRAVATED THE SIT. DECLINING THE REQUEST FOR THE INTXN DEP COULD HAVE AVOIDED THIS SIT. BETTER COM BTWN DULLES GND AND TWR CTLRS COULD HAVE PREVENTED THIS SIT.