Actually I remember hearing about this before, and somebody said it wasn't a perfect game. Kinda surprised me. I'm not really sure though, and I don't even know what the definition of a perfect game is exactly. If it's simply nbody reaching base, then yeah it seems like your example would still count as a perfect game.
"Jack, will you call me, if you're able?"
"I've got your phone number written, in the back of my Bible."