We're also the only team to have traded the first pick. We did so for Kevin McHale (3rd) and Robert Parish.
I'm not sure that this is true. Or, perhaps it's technically true, but there have been draft day trades where the player picked #1 was moved.
Orlando traded the #1 pick in the Chris Webber draft, and Elton Brand was picked #1 and was traded to the Clippers, as well.