It's more subtle than that. LYEDITOR is heeded but EDITOR is not. I'd wager that's a bug.
But the plot thickens now. Running evince from the terminal, it at least tries to use gvim via LYEDITOR. If I run the PDF from Nautilus, the GNOME file viewer, nothing happens. Somehow Nautilus is unable to see the bash environment variables. Yes, I have looged out and rebooted quite a few times. And the strangest part is that I have never consciously configured Nautilus, and furthemore, it all worked fine for emacsclient.
Andrew