Irving Berlin and D# minor

I knew that Irving Berlin couldn't read or write music, but can't believe this from his Wikipedia entry:

In spite of his musical career, Berlin never learned how to play a piano or read music beyond a rudimentary level. He reportedly was unable to compose in any key other than F-sharp major (or, presumably, D-sharp minor, since he also wrote songs in minor keys) and owned a special piano that mechanically transposed keys while an assistant wrote out the music scores.

He could only play in one key? Since a lot of show tunes modulate like crazy, how did he handle that? Did the "special piano" transpose on the fly somehow?

Here's what Wikipedia says:

A Transposing piano is a special piano which can be adjusted by the player (e.g. with a lever or pedal) to transpose. There are not many in existence, but they have been used, for example, by people whose skills are restricted to playing in certain keys, or by those who need to transpose music, but lack the necessary skill in so doing.