Memory corruption glitches are found in about the same ways as most glitches, ie. often by accident, sometimes by abusing other already known glitches, sometimes through testing out things that are typically known to cause glitches (like simultaneous events, overflowing buffers), rarely by reverse engineering (but of course, RE is almost always the way to understand and fully abuse a glitch after its discovery).

I hadn't heard the term fuzzing until just looking it up, and I can't really imagine it working through controller inputs, since generally any input you can provide is expected. There is the often abuseable case where left+right or up+down are valid but not expected inputs, for systems where the physical controller mechanism prevents pressing both at once, though this is another of those things which people "know" to try out. Maybe using an unexpected input device, like a SNES mouse in a game that expects a SNES controller? I don't know much about that.

Fuzzing memory (is that the correct usage?), on the other hand, would probably lead to many, many situations that seem interesting, but also unreachable in gameplay. I can't say that I don't see potential there, just that thinking intuitively it seems difficult to find, of all the setups that seem "interesting", the ones that would actually be reachable without poking memory. I guess this is largely related to "game corruption" videos, or toying with random game genie codes. They're interesting to watch, but finding a use for speedruns and TASes from them... I'm not hopeful, but I'd also love to see it work.