Did customer support confirm that that is the feature they were talking about—watching something after renewal triggers the charge? Or is it possible you were talking past each other? The only documentation on Netflix for this doesn't mention this 'feature' [0], and I can't find any discussion of similar cases (which I would expect for something like this). Also, this kind of behavior would unambiguously violate several existing laws, while most dark patterns are arguably legal (though they shouldn't be).
I'm not saying your dad was lying—it's very possible for someone to click on a button like that (or even two—renew and confirm) and not remember it at all. My dad had a freaky call with what he believed to be Paypal customer support about a scam email, in which they wanted him to give them remote access to his computer. He swore up and down that he didn't call the number in the sketchy email, that he'd looked up the number, but on further investigation he definitely did call the scam number. My dad is a perfectly healthy middle-aged adult, but still misremembered what happened.