They could hit you up with fraud or misrepresentation then, if they really wanted to mess you up. The danger lies on the documents you provided. A GC holder would not need a work permit at all and there is no situation where they would go back to work permits that I know of. It's a pity but companies are really looking into this stuff now because of all the anti-immigration climate when they didn't before (and even to make nice with the government offering to voluntarily do document verification).

I don't know what else to tell you, maybe someone can offer a personal experience with this.