Try fitting that into a click-baity headline! =]

The odds of a collision between an antistationary (BS term, but I'm sticking with it) satellite and another in geostationary orbit are very low. Even though everything up there is in the "same orbit", that orbit has a cross-section of hundreds of miles.

If everything in that orbit were immovable, the antistationary satellite would still be able to avoid it all. Geostationary isn't actually a static orbit. Due to effects from the moon, sun, tidal forces, and plain old voodoo, a geostationary satellite's orbit will incline over time. This requires that it be equipped with thrusters for station keeping purposes.

Should the new satellite fail, there'd be an ongoing effort to track and predict its position and adjust the orbits of other satellites to ensure no risk of collision. (Since geostationary isn't really a stable orbit, anything up there has to have maneuvering capabilities to stay put.)

The real problem is the possibility of one of the satellites up there getting splatted by a passing space rock. It's incredibly rare (I don't know if it's ever happened to anything in GEO or LEO), but would cause the issue you describe if it happened to the new satellite. If it happened to anything else up there, the debris field would slowly be pulled out of GEO and only return every couple of decades.

Not sure it's worth the risk....