I delete my twitter account some time back, since I wasn't seeing the point of it as a regular internet user (ie. not releasing 'important stuff', still having love for traditional rss, not being fond of sharing my latest poop with the whole world, etc.).
Back when I had that account, my updates were linked to my facebook account. Now a new guy registered a twitter account with my old nickname, and HIS updates appear on MY facebook account.
I could probably delete the twitter app from my FB account, but that's not the point. The point is that although my account is suppressed, it is still somehow linked to my personnal FB account.
How lame is that ?
Facebook twitter apps can just scrape twitter for your most recent status update -- if that's the case, they don't even need your twitter password to get updates.
(I don't know how that twitter->facebook app works, but given your situation, that's what I'd guess. So there isn't anything Twitter could do to stop it.)