I would say that's a reasonable way to make that distinction.
well in that case i wouldn't consider you a company just because you hire freelancers. if you are a person who gets gigs here and there and then passes parts of it to someone else for a cut, i doubt that would be called company. however, if your projects come in at a steady and reasonable rate and you pass parts of them to others to do, also at a steady and reasonable rate, then i think you have a company, good sir!
but of course there are other factors as well: 401K, benefits, etc.