I look at it the other way and think of SUVs as a body on a truck frame. I call all the smaller ones that are basically lifted station wagons crossovers.An Expedition is a truck based, body on frame, similar dimensions to a F150. I have a hard time saying its an SUV, like a Rav 4 or Nissan Rouge. Those are more like unibody cars.
I don't know if the first SUVs were on truck frames but when the term got popular most of them were. The Chevy Blazer, Ford Explorer, Suburban, K5 Blazer we're all truck frames. Remember when jeep was the only one that had a unibody for the Grand Cherokee and they used it as a marketing feature (NOT) but everyone actually hated it. Even the Jeep people would have rather had an actual frame or they could have had it easier lifting abilities but the Jeep mentality is such a cult following that they rationalized it and got over it.
I guess it's the utility part of the sport utility that I think means I should be on a truck frame.. The smaller ones that are just cars with rear cargo areas should be called carryalls or multi-purpose.