That's they way I have always seen it as well...which makes Erasure an indie group, even though they make pop music.
You will hear the terms Indie Rock or Indie Pop because the various genres get associated with the independent labels which produced the music.
Alternative rock would be a better term I guess than Indie Rock
Indie pop was a whole scene in itself in the 80s which led to some many good things in UK music.
I think it's more about the DIY attitude of the labels and the bands involved.