I think the lack of external forces' influence on development is the primary relevant factor in "indieness" even if it isn't the easiest to define. I don't think Pub Fund ever affects development beyond accelerating it, which is very different from something where EA comes to you and says "you're going to make a game about Rabbids". Individual deals can be a bit hard to parse since the fine details are probably NDA, but I have no problem calling Pub Fund games indies, or games from "indie publishers" like Devolver, especially when they act more like PR support than initiating and funding development.
For instance, Axiom Verge was in dev for years before Pub Fund. It was probably going to be basically the same game we'll be seeing on the 31st, but it would have taken far longer because Pub Fund let Tom quit his job to work on it. Also Pub Fund is like an advance on royalties not a straight payoff. To me the part where you're clearly no longer indie is when someone else owns the IP--I'm pretty sure Sony owns the exclusive publishing rights for Resogun for instance. I'd call Housemarq indie, but not Resogun. I'd call both Tom Happ and Axiom Verge indie. Not as familiar with Ori's situation.
Also, who the publisher is is an important factor--Velocity 2X's publisher is Futurlab (well...it was, now it's Sierra for the other releases), just like Axiom Verge. Pub Fund doesn't require publishing rights. If the publisher is the developer that's pretty much indie to me--when someone else owns the game is when it's more iffy.