Much as with other things, the problem isn't the creation of the lie, its the publishing of it. I can claim your dad spoke against his values, publish a fake document, draw or photoshop a photo showing him committing a horrendous crime, etc.. Publishing something anonymously as a fake primary document is vaguely new but probably not going to be too common.
It's pretty dumb to suggest that I shouldn't be allowed to create something on my computer privately that I can just imagine on my own, imo.
Notice that I didn't say it shouldn't be allowed; I said it wad wrong and would make me angry. That's an important distinction that is rarely drawn today, between what people shouldn't do and what they shouldn't be allowed to do.
It's pretty dumb to suggest that I shouldn't be allowed to create something on my computer privately that I can just imagine on my own, imo.