Probably a combination of factors resulting on confusion. ... Maybe EDNY gave me somebody else's SID, and Zurich had the right one all along.
I think that's likely. It's easy to say "question anything you're not sure about"; in practice it can be harder, but it's nonetheless important. In your case, asking Zurich to confirm your routing would seem to have been the trick you missed.
Since all IFR airports in Germany are in controlled airspace (or their version of class F), there's always a SID, and you'll always be allocated that in your departure clearance. More often than not, after departure radar will shortcut that or give you a heading.
My last departure with Zurich involved a climb, a revocation of the climb to an intermediate level, and then a further climb, all while flying a strange teardrop horizontally (a ZUE departure from 27 at LSZH). It certainly required more concentration than average!