Earlier quoted context omitted.
Giving a false ID to law enfordement? That is a crime. Giving a forged ID to the secret service, the people in charge of detecting counterfeiting? That's just idiocy. Misspelling department of defense doesnt make the ID ok any more than printing a tiny lol in the corner of your fake dollar bills. (Also, falsely claiming a relationship with the military is downright dishonerable.)
What do you mean by "dishonerable" here? Is this an instance of how Americans love the military so much that it's difficult to understand for people from other countries (where being a military isn't different from being a shop owner, or carpenter or doctor or whatever)?
It's a job, like any other job. People do it because they want to get paid and military worship is ridiculous.