They are "independent" in the way that they don't belong to another major record label...
But "independent" in the same way, as for example, EMI can say they are "independent" because they also do not belong to another major record label and they are their own boss.
It's like a lot of modern "Punk" bands these days...
Sure, they make Music with a "Punk" sound, but do they have the Punk mentality?
