"Rights" are basically just freedoms we've decided we like a whole lot and want the government to guarantee, so that's not exactly a static category. So on the one hand we can just decide whichever rights are being violated are—at least conditionally—not rights. Boom, done.
On the other hand, is there any such thing as a government that does not force people to do things they wouldn't voluntarily do? I'm pretty sure if you take that away what's left has lost the single most important trait of a government, and what's left is... I don't know, a non-profit begging for money on TV and utterly incapable of fulfilling any of the usual roles of a government? In that case, the fact that single-payer would force people to do things doesn't per se remove it from the realm of legitimate government activity.
As for the utility of the term "single payer", I believe it's distinct enough from the much broader "socialized medicine", which could include things like seizing hospitals and making doctors exclusively state employees, to make it substantially more than just a euphemism.