I don't think we should get too bogged down in semantics here. Yes, indie is obviously a contraction of the word independent but over time it has also come to symbolise the general "alternative" label of bands who are outside of the mainstream, so i think both definitions apply.
The big problem is that many artists that fit the "alternative" description signed to major labels or subsidiaries thereof. The Cure are certainly alternative but have pretty much always been on a major label (Polydor / Fiction). Both Sonic Youth and Nirvana signed to Geffen. Radiohead - Parlophone, Manic Street Preachers - Sony / Columbia etc. etc.
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...........