I work at a company that considers itself a startup -- we're seven years old and completely bootstrapped. I've had many people tell me that we're not a "startup," we're just a "normal company." Usually this comes down to people saying that unless our priority is maximizing growth in the short term, we're not a startup. (We are obviously still focused on growth, just not at the expense of our stability, our product, or our company culture.)
"Startup" is a nebulous term with no firm definition, so these kinds of arguments are bound to happen. Some people still say Facebook is a "startup" because it has the fast-paced environment with the normal superficial cultural trappings of a tech startup (food perks, no dress code, casual interpersonal culture, etc. etc.).
Ultimately it's probably just a dumb semantic argument that's best avoided.
