LESS THAN STANDARD SEPARATION BETWEEN 2 ACR. OPERATIONAL ERROR.

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APCHING MSP OUR INSTRUCTIONS WERE DEP FGT HDG 050 DEGS; THEN (AFTER FGT WAS PASSED) WE WERE TOLD TO HEAD 070 DEGS; DESCENDED TO 5000' AND SLOW TO 170 KTS. RADIO COM WAS CLR; SEMI-CONGESTED (ESTIMATE 6 ACFT ON FREQ). ACFT Z WAS TOLD TO IMMEDIATELY SPEED UP TO 180 KTS; WHICH WAS ACKNOWLEDGED. OUR LAST ACKNOWLEDGED INSTRUCTIONS INCLUDED COMMENT THAT VECTOR WOULD TAKE US THROUGH LOC AND TO EXPECT S-TURNS TO OM. WDB ACR Y WAS VISIBLE TO US APPROX 18 MI E OF MSP AND HEADING OUR WAY. APCH CTL GAVE A PARTIALLY COVERED INSTRUCTION; '(SCREECH) TURN LEFT 280 DEGS;' WHICH WAS ACKNOWLEDGED BY VOICE SIMILAR TO ACFT Z. AS WE PROCEEDED 070 DEG HDG ACR Y GOT NEARER AT ABOUT SAME ALT. SINCE FREQ WAS CONGESTED; WE HELD OFF QUESTIONING CLRNC AS WE COULD SEE TFC. ACR Y ASKED APCH WHY WE (ACR X) WERE IN FRONT OF THEM. REPLY WAS THAT WE HAD BEEN GIVEN TURN TO 280 DEGS (AND PERHAPS SOMETHING ELSE); ACKNOWLEDGED IT AND NOT DONE IT; BUT THAT ADEQUATE RADAR SEP WAS PRESENT. REST OF FLT WAS ROUTINE. I CALLED APCH CTL AFTER LNDG AND WAS TOLD THEY DID GET A COMPUTER ALERT AFTER WE HAD CROSSED IN FRONT OF ACR Y AND SEP WAS ADEQUATE. IT APPEARS THAT SOMEONE ACKNOWLEDGED A CLRNC MEANT FOR US W/O IDENTIFYING HIMSELF. COMMON PROB? YOU BET. LATER CALL TO APCH SAID RADAR PLOT INDICATED LESS THAN 3 MI LAT SEP.