If the Eastern woodland natives managed to congratulate both moose and WTD, then North America could become the continent of cervids where they fulfill most of the same roles that bovines do in the Old World.
Well, they'd also have caribou from the subarctic, and at Mayapan there was something with white-tailed deer, so perhaps there's something to that.
I said that it's an interesting theory, as I found it so when I studied it at university, not the Bible. In some cases it works, in others not. Maybe we could say that, if not Carneiro-type places developed an organized civilty, all organized civilities developed in a Carneiro-type places?
I had professors in college who would present ideas like that, and I'd often be one of the students who would discuss counter-arguments in class. Any theory making such sweeping statements is bound to have exceptions.