I was "self-employed" ("Freiberufler") and working for a US startup 100% of my billable hours. They hadn't formed a company in Germany at that point, so I just send them a bill and paid the employer and employee part of my health insurance.

I got some letters about that and they asked me to prove that I was indeed self-employed. They didn't like the argument and concluded that I wasn't. The only thing that actually happened after a while is that I had to pay into the public retirement fund against my will. The "Deutsche Rentenversicherung" are seemingly the only people that care. From what I can tell there were no other obligations/rights that appeared after.