Rights and Freedoms

With respect to the governor vs. the union showdown in Wisconsin, it occurs to me that there's some pretty sloppy talk about "rights" being employed.

While we enjoy the right to peaceably assemble, we have no similar right either to organize as a labor union or to collectively bargain as such.  We have the freedom to do so, but not the right.  A right, unlike a freedom, imposes an obligation on another.

Seriously, what does it even mean to say that I have a right to organize?  Are my fellow workers now obliged to follow suit?  Must they pay union dues whether they agree to or not?  What about their right not to join?  If, as a union, we become dissatisfied with the terms and conditions of our employment and strike, has our employer surrendered thereby his right to replace us all with employees who will work under those terms?

We are free to organize, if we can.  We are also free to collectively bargain, again, if we can.  But it seems to me we have no right to either.