ACR X NON ADHERENCE TO ATC CLRNC (DSCNT TO WRONG ALT) HAD LTSS FROM SMT Y. PLTDEV. TCASII RA EVASIVE ACTION TAKEN.

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ACR X WAS DSNDING IN VISUAL CONDITIONS TOWARDS A LNDG ON RWY 27 AT MCI. WE HAD BEEN CLRED TO 7000 AND WERE ON RADAR VECTORS. WE RECEIVED WHAT WE HEARD WAS A CLRNC TO 4000 BUT THE CTLR DID NOT WAIT FOR AN ACKNOWLEDGEMENT; BUT CONTINUED IN THE SAME BREATH TO ISSUE SOMEONE ELSE AN INSTRUCTION. (OBVIOUSLY NONSTANDARD. HE WAS VERY BUSY; ALMOST OVERLOADED.) THE CAPT AND I CONFIRMED THE ALT AND PUT IT IN THE ALERTER. WE WERE AT ABOUT 9000 FT WHEN WE RECEIVED THIS. PASSING THROUGH ABOUT 6700 FT WE RECEIVED A TCASII RA TELLING US TO CLB. AT THE SAME TIME; THE CTLR TOLD US TO MAINTAIN 7000. THERE WAS AN SMT Y BELOW US AT 6000 FT. WE CLBED BACK UP TO 7000. THE CTLR TOLD US HE NEVER CLRED US BELOW 7000. THE CAPT AND I WERE BOTH POSITIVE HE CLRED OUR FLT TO 4000; BUT OVER THE TELEPHONE THEY SAID IT WAS ANOTHER FLT THEY HAD CLRED TO 4000; NOT SIMILAR CALL SIGNS; HOWEVER. WE WERE ACR X; THE OTHER FLT WAS SAME COMPANY. HE NEVER DID OR WOULD PLAY BACK THE TAPE; BUT SAID THERE WAS NO CONFLICT. OBVIOUSLY; AFTER GIVING AN ACFT A NEW ALT CLRNC; A CTLR SHOULD WAIT FOR A READBACK BEFORE CONTINUING ON. WE SHOULD HAVE CONFIRMED THE ALT EVENTUALLY; BUT WE WERE VERY BUSY ALSO AND THE FREQ ALSO VERY BUSY. WE FORGOT TO QUESTION HIM; BUT PROCEEDED TO DSND ANYWAY. IN THAT SITUATION THERE IS DEFINITELY CHANCE FOR ERRORS TO BE MADE. I WILL DEFINITELY CONTINUE TO READ BACK (AT LEAST ATTEMPT TO) ALL NEW ALT CLRNCS.