No, its not. Its the right to be free of any imposition of government other than that which you are allowed to participate in.
Its not a contortion. Its exactly the whole thing that we get the idea of the right to participate from.
Yes, its possible to have different views of what the right to participate should mean, but they are newer and novel interpretations. That doesn't make them wrong, but they aren't the original understanding, and that original understanding isn't a "contortion".
There's absolutely compulsory behavior going on, even if it's the good kind of compulsory behavior (e.g. setting up structures of power that people have access to).
Unless you want to redefine "negative rights" down until it's "the ones we like, even though people are compelled to do stuff, like create machinery of democracy and not walk onto property claimed by others".
Which, again, ok, if it floats your boat, but it seems more like word games than meaningful discussion about human rights.
The right participate in one's governance is now "the right to participate in government that you can participate in, because without that right the government would be meddling in your stuff".
If people are happy jumping through those kinds of mental hoops to maintain the purity of a "negative rights are the only rights" worldview then ok, but let's be honest about how we're building these flimsy artifices on an idea that can't really support them.