If you ALSO want me to behave like an employee, controlling my hours, sitting through useless HR presentations, and acting like an agent of a corporation, then I'm an employee and I want the full benefit package
Funny, that's exactly what contractors do. I was a contractor for 4 years at a desk where I had to show up in exact hours, attend OIG presentations about sexual harassment and child pornography on business systems, and of course was not allowed to post on Facebook where I work.
In a fair world, none of this should have any relevance to whether one is an "employee" or "contractor". In the past, as an employee I have had huge freedom to work my own hours, and as a contractor, I have worked under a rigidly controlled corporate structure with fixed hours and so on. It all depends on the situation, such as whether regular employees need to have you available during their working hours.
A key difference as I see it is that if you are a contractor, you should be paid at least the loaded rate (i.e. with benefits) of an employee doing the same work. If you aren't, the company is screwing you. And yes, I'm sure many companies are screwing many "contractors" who aren't in a good position to bargain. But I think that should be a primary part of the test of whether a "contractor" is really an employee.