That hilariously restrictive definition would have classified my old beast of an ex-military cargo vehicle as a "minivan", but I doubt you'd convince any onlooker to label a vehicle like this as anything other than a "truck":
Yeah - technically. But this whole discussion is about the consumer space, not about those purchasing commercial equipment for hauling tonnage or whatnot.
Even so, though - there are plenty of consumer pickup models which are used commercially, and more than a few can handle some pretty big loads (especially towing)...
For me, having a permanent bed cover means it's not useful as a truck.