That's true as long as you do not wish legal status of any kind for your 'partner' over and above what a stranger would have. Otherwise, the government does have business defining what marriage is.
I could grant my partner (my wife, in my case) any kind of special legal status I want. For instance, she might designated me her health-care proxy, and I could do the same for her.
Similarly, two men could designate each other with all sorts of special relationships under the law through mutual contract, and do so all the time. If this constitutes marriage, we've had gay marriage for the last twenty years.