> In quite a few countries, a false positive can lead to someone getting put in prison
That can only happen if it is either (1) used by government, or (2) used by private entities in a process flow that includes reports to government.
"There exist countries with criminal justice systems with weak enough standards of proof that a false positive on a scan alone would result in prison", even if 100% true, is not a justification for a firm not making efforts to block child porn distribution on its networks. (It is, OTOH, a justification for working to reform the criminal justice systems in those countries, but that is rather far from the topic here.)
It's all a matter of 'the image hash was on the database, therefore OP is guilty. 10 years incarceration'.
I wouldn't want to be enabling such a system.