Wait, I think I have debunked the patch thing. It's apparently a "morale patch":
[link to milspecmonkey.com]
(See third row from the bottom)

If the "happy customers" on this website are any indication..it appears that military men and police officers and the like buy those patches and put them on their uniforms to look cool. Not necessarily a "fake" official badge, just something he thought looked cool. And maybe his "official" badge is on the other side we can't see.