OK so in The Nanny, they have a limo, right. And the Wiki says Niles is their chauffeur, but he's always inside when "the limo is waiting". WHO DRIVES IT? WHO?

Further conflicting evidence

Niles (who is definitely the butler) does drive the limo (and wears the hat) in the episode where they get snowed in at Sylvia's apartment.

But as @BlytheByName points out, when Grace "takes the limo" to the same apartment in a different episode, Niles doesn't know she's gone.