They actually are not capable of generating garbage, there is no such entry made in any pokedex game, television or manga, they are garbage brought to life capable of absorbing garbage, it is you who is wrong good sir
"or Garbodor fires multiple globs of sludge surrounded in a gold aura from its mouth at the opponent."
Your point being? Garbador is made from and consumes garbage. It just uses its stores for the attack. Also, every version of the attack in the games shows the "garbage" (purple gunk) coming from the attacker's body, mouth, whatever, directly. One strange visual representation of the attack in the anime, known for its inconsistency, doesn't make it a user.