You are, presumably, referring to Gennadios Scholarios. And you're claiming that he specifically recognized Mehmed as the successor of the Byzantine Emperors, and not merely acknowledged him as a conqueror of the city? What is this idea based on?
My bad, I confused Gennadios with George of Trebizond.
In any case, the Ottoman chancellery fairly consistently used the Greek title
basileus and the Latin title
dei gratia imperator to refer to the ruler whenever they had correspondence in Greek or Latin up to the mid-sixteenth century, as well as the Turkicized title
kayser i-Rum, so my point still stands. Curiously, Mehmed II himself did not call himself
basileus in Greek for whatever reason (he preferred
o megas authentis kai megas amirus, "the great lord and great emir").