Scott, perhaps Terry takes an even more traditional view than you? Is it not correct that NY-style pizza originally contained neither oil nor sugar?
As I've said many times before, I don't subscribe to the 'elite' NY style classification and 'street.' I call early NY pizza 'coal' style. Coal style typically contains neither oil nor sugar. But his favorite pizzeria, as I said, was Joe's, and Joe's isn't coal style, it's NY style. I know, for a fact, that Joe's isn't naturally leavened, but I can't say with absolutely certainty that it contains oil. Based on the way it browns, though, I'm 99.9% certain.
In other words, when Terry says authentic NY style pizza can't contain oil, Joe's is part of that list- and places like Joes- along with, of course, coal. He can say that about coal (or 'elite') all he wants, but Joe's is NY and NY contains oil more than it doesn't. In fact, I would go as far as to say that oil is only second to bake time when differentiating between coal and NY style pizza. And, considering coal's renown for inconsistent bake times, oil might even have a bit of an edge.