Some years ago I read an article on Toms Hardware (can't find it now) testing power supplies. It was a eye-opener, such as how the manufacturers made "creative use" of the specifications or outright lied. What I read concerned longevity and reliability of the motherboard regarding nice stable supply voltages. I started using Seasonic exclusively after that.
When testing my previous rig for overclocking, I found the mosfets on the motherboard needed better cooling to run stably at speed. Various guides point out that the frequency changing when the cpu idles, and the anti-interference clock jitter can cause crashes because two clock ticks may happen to close together. Voltage fluxuations make that worse and overclocking literature reports that it does make a difference as to running stably.
So, it is plausible that at rated speed it might matter as well, especially if the computer is running too warm.
In an extreme case, a low voltage can crash the cpu by browning out.
As for power to the power supply: in a well-made psu it should not care. However, some of the stuff missing from the cheap ones are exactly the parts to smooth out fluxuations and buffer against rapid changing of the inout voltage.
Here is an anectode I heard a number of years ago: all the computers in the room would crashnat the same time except for 1. Upon close inspection, they all, had the mains voltage switch set wrong except for the good one. Set for 220 input but feeding it 110 worked just fine under ideal circumstances, but not when (presumably) something happened like under-voltage or excessive line noise. And the power issue made the machines crash.
So what could be wrong with a power strip that would induce such problems, while a different strip was fine? I can think of intermittent contact, or insufficient/burned-out noise filtering and surge protection. Something else plugged in to it might supply surges or line noise.