Opposition is against building GLONASS monitoring stations on US soil; not against GLONASS or any indigenous navigation system itself.
- Tons of military bases (see: all over the world)
- NSA mass surveillance centers (see: Germany, and probably secret ones elsewhere)
To give you an idea of reference stations in the US for the GPS system, head on over to: http://www.ngs.noaa.gov/CORS_Map/
Granted, these are used for post-processing position data for increased accuracy, and not for updating mission-critical orbit/atmospheric error data, but the principal is the same.
>“They don’t want to be reliant on the American system and believe that their systems, like GPS, will spawn other industries and applications,” said a former senior official in the State Department’s Office of Space and Advanced Technology. “They feel as though they are losing a technological edge to us in an important market. Look at everything GPS has done on things like your phone and the movement of planes and ships.”
> The Russian effort is part of a larger global race by several countries — including China and European Union nations — to perfect their own global positioning systems and challenge the dominance of the American GPS.
There is a giant network of ground stations around the world so that french submarine can re-calibrate their positioning system periodically. It's a unique solution that only works when you have territories all over the world, since you don't want to position your nuclear power with a foreign system.