I suspect this is a revenge fantasy rather than something that actually happened.
As for who's responsible - it's a mix. Some people who deal with these situations are doing their jobs because they have no choice.
Some are active sadists and do the job because they get to bully the weak.
This happens a lot in benefits management, and also in immigration, in most countries.
You underestimate government inefficiency. You are correct, but I can also see a system that naively prints whatever is verified as a valid entry automatically.
I'm not so naive as to think there's no podunk, crossroads "town" out there that has some mayberry-ass fax machine just spitting out whatever you send it. But given how attractive government offices are to people for either pranking or ...ahem redressing via their fax machines since the late 70's, it's more common than you might believe for even the smallest little townships to have a contract with a company that turns faxes into emails.