It's not just that bands signed to independent labels, many independent labels were bought by the majors, meaning some bands went from indie to not indie overnight (according to the original definition of the genre anyway)
Indie became popular in the 80's, the majors saw this and bought labels to get the bands. But hang on, the bands were popular, therefore they must be pop...........
Haha...and around and around we go
Actually, if was often the other way around - the indies sought out deals with the majors because as their artists got bigger they couldn't handle the increase in cost and in marketing, distribution and physically pressing / packaging the records etc.
The indies were often victims of their own success in a way. When they had artists selling handfuls of records the indie label bosses could practically do everything themselves, including packaging the record sleeves. Not so easy to do when your artist is selling half a million copies!
Of course the major labels did want to jump on the "indie" bandwagon, in some cases as far back as punk (as we all know with the Sex Pistols being touted to all and sundry) and several of them created offshoot subsidiary labels specifically for the purpose of signing independently-minded artists, so Polydor had Fiction, Warners had Blanco Y Negro etc.