ACR X HAD LTSS FROM ACR Y WHILE LNDG AT DCA MULTIPLE RWY OP INTERSECTING RWYS. SYS ERROR.

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ACR X ON APCH (IMC) CTLR CHEWED OUT ACR Y FOR NOT KEEPING HIS SPD. TWR CTLR SENT HIM AROUND DUE TO SPACING. HE WAS SEVERAL ACFT AHEAD OF US. THE APCH WAS TIGHT; ACTUAL CONDITIONS AT THE 3 MI POINT WAS APPROX 9 OVCST 2 1/2 RF. WIND RPTED BY TWR 320/10 BUT FMC WIND AT 900 MSL WAS 340/18. VISUAL CONTACT WAS MADE; WX AT AIRPORT WAS BETTER THAN 1000/3 IN R-F. TIGHT TURNS TO FINAL RWY 18; FMC WIND AT 300 MSL 310/12 (TAIL WIND LDG). AT 200 MSL TWR ADVISED TO ROLL TO END OF 18; DO NOT TURN ONTO CROSS RWY. RWY WET; QUARTERING TAILWIND; HVY ACFT; TIGHT MANEUVERING; CONCENTRATING ON PROPER SPD AND TOUCH DOWN POINT AT 1000 FT POINT. NORMAL REVERSE; LIGHT BRAKING; AT APPROX BESIDE TAXIWAY 'M' TWR ASKED WITH A SENSE OF URGENCY 'CAN YOU HOLD SHORT OF RWY 21?' AT THAT POINT I CAUGHT A GLIMPSE OF MOVEMENT AT MY 8 O'CLOCK POS AND REALIZED ACR Y WAS IN THE FLAIR ON RWY 21. FO ADVISED WE COULD HOLD SHORT OF RWY 21. MAX ANTI-SKID BRAKING; MAX REVERSE THRUST; STOPPED AT TAXIWAY 'F' AS ACR Y CROSSED IN FRONT OF US AT HIGH SPD. CABIN FILLED WITH ODOR OF TIRES; WATER COVERED COCKPIT FROM REVERSE THRUST. AT NO TIME DID TWR ADVISE US OF CONFLICT. IN MY JUDGEMENT ACR Y PROBABLY COULDN'T HAVE GONE AROUND OR STOPPED SHORT OF 18. I BELIEVE LCL CTLR SAW HIS ERROR AND DUMPED THE PROBLEM ON ME BY ASKING ME TO HOLD SHORT OF 21 AFTER PREVIOUSLY DIRECTING ME TO END OF RWY. NO FARS WERE BROKEN. SUPPLEMENTAL INFO FROM ACN 190276. ON FINAL APCH LDA. DME RWY 18 AT DCA; WE HAD JUST BEEN SWITCHED TO THE TWR. WE WERE NEAR OUR FINAL APCH SPD. I HEARD THE TWR ISSUE A CLRNC TO THE ACR Y; (TURBOPROP) TO GAR. THE TWR CTLR THEN ASKED ACR Y (WHICH HAD BEEN ON THE LDA-DME 18) IF HE WAS ABLE TO CIRCLE TO RWY 21. ACR Y REPLIED 'AFFIRMATIVE.' I THEN CALLED THE TWR AND WAS ISSUED A CLRNC 'CLRED TO LAND RWY 18.' WE WERE STILL IMC AT 1500 MSL. AT 1000 FT WE WERE ABLE TO SEE THE RWY WITH LIGHT RAIN. THERE WAS APPROX A 15 KT TAILWIND AT 1000 FT. AT 200 FT THE TWR CTLR TOLD US TO ROLL TO THE END OF THE RWY 18 ON LNDG ROLL. JUST AS WE WERE TOUCHING DOWN (WITH A 9 KT TAILWIND COMPONENT AND WET RWY) THE CTLR ASKED IF WE COULD HOLD SHORT OF RWY 21. I LOOKED OVER AT THE CAPT AND AFTER MOMENTARY CONSIDERATION HE SAID 'TELL THEM WE CAN.' THE TOUCHDOWN WAS VERY NEAR THE 1000 FT MARKER. THE AUTOBRAKES; WHICH WERE PREVIOUSLY SET ON #3; GAVE US GOOD DECELERATION. THE THRUST REVERSE WAS IMMEDIATELY USED IN MODERATE AMOUNT. I THEN NOTICED THE CAPT BRING THE REVERSE LEVERS TO MAX REVERSE AND APPLY VERY HVY BRAKING. AS WE STOPPED; STILL USING MAX REVERSE THRUST; WE WERE ONLY ABOUT 200 FT FROM RWY 21 (THE INTXN). I THEN CAUGHT ACR Y OUT OF MY L SIDE; ROLLING OUT L TO R ON RWY 21. IF THE CAPT HAD NOT USED EXTREME STOPPING MEASURES THERE WOULD HAVE BEEN A COLLISION. I FEEL THE CTLR WAS ATTEMPTING TO COVER HIS ERROR BY REQUESTING THAT WE HOLD SHORT OF RWY 21 AT THE LAST MOMENT; HE DID DURING OUR TOUCHDOWN. I ALSO BELIEVE THAT; IF THE CAPT OF MY ACFT HAD SAID HE WAS UNABLE TO HOLD SHORT OF RWY 21; THAT NEITHER ACFT WOULD HAVE BEEN ABLE TO GAR PRIOR TO THE INTXN. THIS WOULD HAVE CAUSED A COLLISION WITH ONE OR BOTH ACFT IN THE PROCESS OF A GAR AFTER LNDG. OUR ONLY CHOICE WAS TO STOP!