Veronica actually made the decision not to look, btw, it was Keith who later issued a paternity test of his own.

Oh, right, my bad, I misremembered. I do remember being also a bit annoyed that they had Jack conduct a paternity test and then tell Sydney he'd love her no matter what, but yes, he's her father, in season 3, because that statement would have been a lot more powerful otherwise (and no less true), but it did make character sense for Jack to have that test made, so I went along with it.