Electronics tend to fail at dosages (20 greys or so) similar to what destroys your nervous system.

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.

[dead]