I recall Bruce Schneier writing [1] about a friend of his who had a custom ID card made identifying himself as an ambassador from Mars. It supposedly works way more often than it should.
[1] I don't have the citation and search engines aren't helping. I suspect it was in Beyond Fear.
Woz had a Department of Defiance ID that he used to get into all kinds of places. Apparently it's not illegal because it doesn't actually say 'Department of Defense' so it's not a counterfeit ID card.
IANAL, but I think the legal definition of fraud would make that illegal. You're getting something by deception, since you know the person thinks it says Department of Defence.
[1] I don't have the citation and search engines aren't helping. I suspect it was in Beyond Fear.