I see where you're coming from.
I see them more as both being South Park joke songs and not really looking at the actual "band" because in this case it isn't really a band.
Kind of like if we got a Sponge Bob song sung by Patrick, it would still be like a Sponge Bob song and would fall under that umbrella.
Plus it takes a song of the list of rb1 songs with no dlc that otherwise would never come off.
Just thought I'd fully explain my view on it since my first post was brief.
Now with the greenday/the network situation, I fully agree those should be separate because they are in fact different bands. It's not like the case with Vagiant/Tiajuana Sweetheart band where they just changed the name and the slash makes sense.