I think it's a good rule of thumb. When they send robots into something like the Fukushima site they don't last long.
My first take is that I'm not surprised from a fermi problem standpoint that you can destroy two computers made from small parts smashed by radiation with a similar dose. But maybe that intuition is wrong because your brain could survive losing a few neurons but a microchip could be 0% functional after losing one transistor. My rule of thumb is about right for conventional chips but you can certainly get rad-hard chips that hold up better:
They absolutely could, and only one robot got disabled by radiation. The problem was that robots of that era were nearly useless.
Why they were useless is interesting in itself. It turned out that controlling robots, when all you have is a bad TV camera, is hard. And robots also tend to get stuck on things.
As a result, the "Joker" robot that was helping to clear the roof got its tracks wedged on a firefighters water pipe.
They could, if they were specced correctly. Wasn't the story that they intentionally requested robots hardened against lower radiation level than required to not disclose the true extent of the catastrophe? So the German company that built them underspecced the shielding and so they died quickly.
That doesn't quite dovetail with the story I've heard about them shooting the elephant's foot with a gun to spall off a sample. I think there's still some damage control in some of the stories.