Indie is a bit of a weird definition. Is Valve "indie" just because they have production, publishing and distribution all under one roof? Technically, yeah, they are.
The thing is, Indie no longer truly means "independently produced" (i.e. without influence from outside creative forces) - it has become a genre of its own, mostly defined by its experimental gameplay, minimalistic or highly specialized technical framework, little to no marketing outside the raw basics, and original (or retro) art direction. EA could produce a game like that and you could bet that the word "indie" would still appear whenever anyone talks about it (and be it in the sense of "indie-ish").
The thing is, Indie no longer truly means "independently produced" (i.e. without influence from outside creative forces) - it has become a genre of its own, mostly defined by its experimental gameplay, minimalistic or highly specialized technical framework, little to no marketing outside the raw basics, and original (or retro) art direction. EA could produce a game like that and you could bet that the word "indie" would still appear whenever anyone talks about it (and be it in the sense of "indie-ish").