I'm really not sure and I could be wrong, but I wonder if that person called cats "false" pets because they really haven't been domesticated(sp?) very long at all, and can easily return to being wild if conditions force them to do so.
People who don't understand cats often think of cats as being aloof -- that could certainly contribute to their thinking of cats as not qualifying for the name "pet" -- if they'd only give them a chance.
I agree, I think cats are pretty real too. People like have never met a cat like Toes. But then maybe they're false pets because they're more like family rather than a pet?