... on the highway, i doubt you get that much side wall movement because the roads are usually pretty straight, so there's no lateral loading of the tire....
Yes, you do get a lot of sidewall movement with an underinflated tire at highway speeds, and it has nothing to do with lateral loading.
Look at a tire at low air pressure at standstill: the sidewall is bulged out at the point of contact with the road, due to the weight of the vehicle. But the sidewall of the tire opposite the point of road contact is not flexed or bulged outward. Roll the tire one revolution, follow the sidewall at one fixed spot, and you'll see the sidewall at that spot move - flexed outward at road contact, not flexed, flexed out again.
It takes 600 (or something like that...) revolutions of the tire to cover one mile - so in one mile, the tire sidewall goes thru 600 cycles of flexing outward and coming back. That can generate heat; at trail speeds, that heat dissipates easily. At 60 mph, that is 1 mile per minute, or (if we stay with the number above) 600 flex cycles per minute, or 10 flex cycles per second, heat is not only generated rapidly, but doesn't dissipate as easily any longer. So you have a lot of sidewall movement with an underinflated tire. There's always some movement in the sidewall, but you'll get more with lower tire pressure.
Whether this is going to kill a tire is dependent on many variables, tire pressure / speed / tire size / ambient temperature / sidewall construction / tire materials come to mind.