i like nickel creek, but I never caught the fiona apple wave i guess...that seems like a strange combination unless one or both of the bands changed their sound a lot!
I think they meet in the fringe of alternative stuff. Nickel Creek does a lot with Toad The Wet Sprocket and John Paul Jones... so Fiona isn't much of a stretch from there.
Plus Chris Thile has been known to gig with Fiona and cover some tunes...