Frames flex, the Tundra frame really flexes.
I've got a '95 T100 Xtracab with the 5VZ-FE sitting in the driveway right now, fully boxed frame front to rear and it has tons of chassis flex/deflection.
No, this isn't a matter of boxed vs. C-channel, this is a matter of basic frame construction. Toyota went cheap on the new Tundra in many ways, the frame was one of them. Notice the 4-star crash test results from NHTSA.
Ford built a much better full-size truck frame than Toyota, that much is obvious. If Toyota skimped out on the frame, what else did they go cheap with?
Even look how the rear shocks mount to the frame on the half-tons, Ford does it in a far superior way to Toyota.