APCH CTLR GAVE AN ACR B757 AT 14000 FT A TA ON A BE36 VFR AND CLBING TO 13500 FT. THE B757 SAID HE HAD A TCASII RA AND WAS RESPONDING BY CLBING TO 14500 FT. B757 WAS UPSET WITH BOTH THE APCH CTLR AND THE BE36 AND ALLEGED AN NMAC. BE36 PLT SAID ACFT WERE NO CLOSER THAN 2-3 MI AND HE NEVER EXCEEDED 13500 FT.

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ACR X (B757) WAS LEVEL AT 14000 FT AND RPTED AN RA ON HIS TCASII. TFC HAD BEEN ISSUED; A BONANZA (SMA Y) THAT HAD CLBED TO 13500 FT TO STAY VFR. ACR X TCASII INDICATED THE TFC AT 14000 FT AND HE CLBED TO 14500 FT. SUPPLEMENTAL INFO FROM ACN 350255: I ADVISED MCO APCH THAT I REQUIRED A CLB FROM 12500 FT TO 14500 FT. SHE REPLIED (THE CTLR) TO MAINTAIN 12500 FT. I REPLIED; 'UNABLE TO MAINTAIN VFR AT 12500 FT.' SHE REPLIED; 'UNABLE 14500 FT DUE TO TFC; CLB AND MAINTAIN 13000 FT.' I REPLIED AND CLBED TO 13000 FT. AT 13000 FT; I ADVISED 'UNABLE VFR AT 13000 FT; IFR EQUIPPED AND QUALIFIED.' SHE REPLIED; 'MAINTAIN VFR; CLB AND MAINTAIN 13500 FT.' I COMPLIED AND CLBED TO 13500 FT. IN BTWN 13000 FT AND 13500 FT I OVERHEARD THE B757 CAPT STATE THAT HE HAD A 'TCASII AND AN RA' WHICH REQUIRED HE CLB IMMEDIATELY TO 15000 FT AND THAT HE HAD NOT SEEN THE 'BONANZA.' 2 OR 3 MI AHEAD AT 1 O'CLOCK; I SAW A LARGE JET IN A CLB AND RPTED THE 'TARGET IN SIGHT.' THE B757 CAPT BICKERED WITH THE CTLR ABOUT THE RA DEV AND ASKED FOR THE BONANZA TAIL NUMBER. BECAUSE I WAS CONCERNED ABOUT WAKE TURB AVOIDANCE I ASKED THE CTLR; 'WHAT TYPE JET WAS IT THAT HAD GONE BY.' THE B757 CAPT ALSO ASSERTED THAT HIS COMPUTER 'PUT THE BONANZA AT 14000 FT' I DO NOT BELIEVE THERE WAS AN NMAC OR VIOLATION OF CTLR INSTRUCTIONS. I BELIEVE THE B757 CAPT WAS UPSET BECAUSE HE HAD TO DEVIATE FROM HIS ASSIGNED ALT BECAUSE OF HIS TCASII RA. I DO NOT BELIEVE HE EVER SAW THE BONANZA.