So, the only way to manipulate it is to actually screw with the internals of the CPU itself by "glitching", meaning tampering with the power supply to the chip at exactly the right moment to corrupt the state of the internal electronics. Glitching a processor has semi-random effects and you don't control what happens exactly, but sometimes you can get lucky and the CPU will skip instructions. By creating a device that reboots the machine over and over again, glitching each time, you can wait until one of those attempts gets lucky and makes a tiny mistake in the execution process.

Considering that the PSP is a small ARM processor that presumably takes up little die space, would it make sense for it to them employ TMR with three units in lockstep to detect these glitches? I really doubt that power supply tampering would cause the exact same effect in all three processors (especially if there are differences in their power circuitry to make this harder) and any disrepancies would be caught by the system.

I was going to say I disagreed but the rest of your comment reminded me that I've accumulated a lot of domain-specific knowledge.