It didn't originate with me, although I'm pretty sure it's true. Usually absolute termination of parental rights isn't done except for the most severe danger to the child. You'll occasionally hear stories about some rich family who has their daughter get knocked up by someone so undesirable even a shotgun wedding isn't on the table, and they'll give him a choice of very bad things happening to him or taking a payoff to go away forever.
I think he agreed to it because while his behavior was atrocious, it still ended up pled to a disorderly conduct charge. It wouldn't have justified terminating parental rights entirely by itself. They'd usually just give full custody to the mother. So I think he not only had to have agreed to it but to the factual basis for it.
Family courts don't like terminating parental connections entirely and permanently, because this can end up meaning the kid ends up in the state's care and can't get child support. So the "best interest of the child" analysis they go through means they literally thought the child would be better off having no contact with her biological father than having this fat piece of shit as a father. Also, she had a second, better father by that point.
They also really don't like the idea of a father just shrugging off his obligations and walking away scot-free.
Anyway, I think it was an inference someone drew and I agree with it. I think it's almost certain he had to sign off on it.
But family court records are often not available to the public, especially when they involve the details of minors.
If not, he did something even more fucked up than the threats.