If you watch one of her interviews on it she even says she has had record deals but they have all fallen through the cracks. And a lot of them have had past chances in the industry, in fact that's how NBC finds them (watch the blind auditions eps.)
Either way her voice is so different and unique that she deserves a shot like any other person. And as someone else put it on here Automatic Love letter and Meg&Dia may be big to us on the forums but the general masses don't really know who they are.
She's definitely mentioned that she's been dropped from various record labels/deals. And I think being a Mouseketeer/ associated with Alicia Keys has more name recognition to the average TV viewer than being in a broken up scene band.