B737 LNDG CLE IS GIVEN LAST MIN RWY CHANGE BECAUSE OF AN APPARENT CTLR ERROR OR MISJUDGMENT.

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ON ARR INTO CLE; ATIS ADVERTISED VMC; ILS RWY 24R. WE SET UP AND BRIEFED ILS RWY 24R IN VMC CONDITIONS. UPON ENTERING CLE TERMINAL AIRSPACE WE WERE TOLD TO EXPECT RWY 24R. WE WERE VECTORED TOWARD THE RWY AND SOON CLRED FOR THE 'VISUAL RWY 24R.' AS WE CONTACTED TWR AT BECAT (THE FAF); TWR THEN CLRED US TO 'LAND ON RWY 24L;' A COMMON PRACTICE HERE IN CLE TO HELP EXPEDITE TFC. THE CLRNC WAS READ BACK AND THE FO AND I SET UP FOR THE NEW RWY; WITH ME; AS THE PF VERIFYING WITH THE FO THAT WE WERE NOW GOING TO LAND ON THE 'INBOARD RWY 24L.' WITH THE ACFT WELL STABILIZED; AT APPROX 1000 FT ATC THEN CLRED A B737 INTO POS AND HOLD ON RWY 24L. THE FO AND I NOTICED THIS AND DISCUSSED THE POSSIBILITY OF A SIDE STEP OR GAR. A FEW MOMENTS LATER THE TWR CALLED US STATING 'CLRED TO LAND ON RWY 24R NOW...SORRY IF I HAD CLRED YOU TO LAND ON THE L...CLRED TO LAND RWY 24R OR GO AROUND IF YOU CAN'T DO THAT!' I ADVISED FO THAT I WAS COMFORTABLE WITH THE SIDE STEP AND WE ACCEPTED IT. I MANEUVERED THE ACFT TO THE R; REESTABLISHING ON THE VISUAL GS AND WE LANDED WITHOUT INCIDENT. WE DEBRIEFED AS A CREW AND I INITIATED A CALL TO THE CLE TWR TO DISCUSS THE EVENT WITH THEM. I WAS TOLD THAT THEY WERE 'TALKING ABOUT IT.' I GAVE THEM OUR ACCOUNT AND ASKED IF THEY NEEDED ANY MORE INFO FROM ME. I WAS TOLD NO; AND THANKED THEM FOR THEIR INPUT. THE FO AND I DISCUSSED THE EVENT FURTHER AND FILED AN ASAP.