I've seen news stories about pets getting credit card offers, so I can believe it.
DS #1 got a pre-approved credit-card application when he was 11.
What else to do? - he filled it out and sent it in (and we knew about it, we were kind of curious to see what would happen). He was very honest; his annual income was around $150 (his allowance) and he listed his occupation as "child labourer". Also, his printing was definitely typical of an 11 year old boy.
About 10 days later he got a phone call. "Mr. xxxx, we have your application and are in the middle of processing it and are all set to approve it. We just need to know - you seem to have made an error on your birth date". The operator repeated it, and he acknowledged that it was correct. "But that would mean that you're only 11!" "That's right." "Uh - could I speak to your mom or dad?"
I wasn't home at the time (I wish that I had been) but Dh was and he verified that yes, they had indeed sent a card application to an 11 year old. Of course it went no further than that, and the caller said that she would definitely bring this "error" to her supervisor's attention.
Re the OP - IMO these people were definitely to blame when they listed the cat on the census. Even if they were doing it jokingly rather than trying to claim the cat as a dependent, they were really the cause of the problem, rather than bureaucrats.