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.