Alright, I think I'm pinpointing it now.
On "Bizness," for example, particularly when she sings the "don't take my life away" line... She's not from Africa, and she doesn't have an African accent... so why is she putting one on so deliberately? I can buy the style emulation, but to take on even the vowel inflections is annoying. It's the same thing that annoys me about some white pop/R&B singers (e.g. Rebecca Black, Justin Bieber, and many others), who will sing things like "we so excited" with a straight face. Yes, I just compared Merrill Garbus to Rebecca Black... and while I don't think Merrill Garbus is nearly as bad, for me she's on the same spectrum. The fact that she admits as much doesn't make it less annoying.