My wife plowed into the side of another car, and although the truck (2001 Toyota Tacoma Doublecab TRD V6) had some damage it was not "totalled". The frame is bent pretty badly. The insurance company told me “Toyota says that Straightening their frames is perfectly acceptable” I’m concerned. Does anyone know if straightening a frame will cause weakness or future problems… or what Toyota’s official viewpoint might be? I use this truck very heavily: off road on the farm.

~Rob

Frame Straightening works.
Is the area straightened weaker? Yes, always. But the weakness is marginal.
Remember, everything is typically "over-engineered." The marginal weakness, especially in the frontal areas where she plowed into another car, will not effect performance in the future, even under a heavy load.

Your farm use implies heavy loads downwards in the box area. No problem. Or heavy towing (shear) forces. No problem at the back.

Go for it, and for god's sake...don't worry.