Today, sure. It wasn't always. Alternative in the 80s was pretty much "rock, but too weird and smart to be played on the AOR/classic rock stations, and not on a major label". That might sound like "dumping ground" as you described, but it wasn't really -- it was a fairly coherent genre for a while, until everything started being called alternative if it wasn't pop or mainstream hard rock, etc.
Classic rock stations would play Guns 'n Roses, Def Leppard, but not R.E.M. or Concrete Blonde, and certainly not Rollins Band, for instance. There were no alternative rock stations, at least in/around St. Louis, excepting the college station (KDHX, 88.1).
Legit alternative: R.E.M., Robyn Hitchcock & The Egyptians, The Replacements, The Smithereens, The Smiths, B52s, XTC, Concrete Blonde, Echo & The Bunnymen, Pixies, Dinosaur Jr, plenty of others. In the late 80s and early 90s, after R.E.M. and others had commercial breakouts, the genre was muddied beyond recognition. Especially with the advent of grunge and more accessible industrial music like NIN.