I know there is a notorious, random black screen issue with certain newer AMD Radeon cards, such as 5700/5700XT. Some people never or almost never get it, some get it more often.
I don't know if it is GPU-Z related though.
I am getting a Google Chrome black screen occasionally here, but it is unrelated to GPU-Z. Leaving the PC unattended for 10-20 mins often shows me a completely black screen, but this is just Chrome, not the whole PC display getting black. Closing Chrome and running it again fixes the issue.
(And card here is quite old - AMD Radeon R9 390.)