The phrase "you can't prove a negative" is really short-hand for "you can't prove a negative existential claim within an effectively infinite scope", ie. I can't prove that Bigfoot doesn't exist anywhere in the universe simply because absence of evidence is not evidence of absence.

But I can easily prove that Bigfoot does not exist within my coffee mug, or that a particular box I have which contains 5 pennies contains no silver dollars, or that the list of suppliers with whom I directly do business does not include "Missouri Correctional Services LLC" (and I think the spirit of GP's suggestion is boycotting companies that directly do business with prison labour, not people who transitively do business with it at a 25 company remove, or something)

In this case, auditor certification of the supply chain.