Nope, not buying that levitation is a necessary consequence of telekinesis. It's one that's easy to justify within the rules of the world, but I don't think TK inherently implies levitation unless we've been told it does, which we haven't.

Again--you can pick up objects, like a pencil. So by your logic, you should be able to pick yourself up just as easily, so you should be able to levitate as long as you had a good grip on yourself.