I can imagine that by fraudulent they mean if the president is provably mentally incompetent or literally physically unable to sign, or a pardon is produced that cannot have been signed by the president due to other factors at the time of granting the pardon. But as said I'm not an expert, I just remember reading it.
also, New Hampshire went democrat, right? since your picture shows it has a full republican governmen and you said this:
So that's the one exception then?And any state that has a Republican Governor and Legislature is almost certainly already voting for a Republican presidential candidate anyway.