Do you have this backwards? Any animal can be "undocumented", and there are in fact strict requirements for cattle documentation if they're to be used as food.

Do you have this backwards? Any animal can be "undocumented", and there are in fact strict requirements for cattle documentation if they're to be used as food. But only humans can be criminals. More relevant is perhaps the issue of accuracy - if a US citizen loses their ID, they are "undocumented". Meanwhile an illegal immigrant, even if they have all their papers and the authorities know who they are, i.e. they are fully "documented", is still not permitted to stay in the country.