I don't think it really makes a difference. Husker Du was the first of the American 2nd generation punk bands to go major label. They did it merely because the distribution of their products through SST was horrendous. Bob Mould later helped others, such as Sonic Youth, make the same type of transition.
Bands like Rush, who have controlled their own production from the beginning, raise the question: are they major label or independent? While their distribution is major, their content is not.
Then there are the bands like The Church who started on major labels and are now on indie labels. The Church had their Arista years where they were pushed to the breaking point, but it did yield Priest = Aura, arguably the most popular among their fans. While it's singles Ripple and Feel did get some airplay, they only charted only on the College charts. Now we would call them alternative, back then, they were just not popular.
That said, most of what I listen to is not played on the radio. At least, not out here in the sticks. The only thing I ever hear broadcast is news on NPR. Most of the stuff I own is from small labels, but is there a stigma attached to a large label? There are still folks at those places that love what I consider good music and they can have a few bands signed that are never going to make anyone rich.
If Ke$ha can fund a few good bands, go baby go.