Bilotti was not the underboss, he may have been Castellano's driver and gopher, and may have even filled in briefly after Neil died, but he certainly was not going to be Big Paul's second in command for the long term future.
Who knows if Bilotti would have been the long term underboss, but he replaced Dellacroce in that position, didn't he? The main reason it was brief was because he was whacked.
