The defect in your reasoning is that Obamacare is forced upon you by the government. You must comply or face punishment. It isn't a voluntary contract with mutually beneficial characteristics. It is blackmail on pain of lost of liberty and property.
I completely agree with your point; thus my repeated attempts to emphasize that the gummint is the one institution not to trust in this role.
I should have emphasized that more.
As you state, Obamacare does not give us the choice on our healthcare (except an abortion ...)