To get approval in US and Europe, the trials need to be of the same quality no matter where they are run. Sometimes it may be cheaper in poorer countries because you don't have to pay your volunteers as much. You still need to check all the appropriate boxes regarding informed consent as anywhere else. And, of course, western companies are entirely capable to run trials anywhere in the world. The COVID vaccine trials were run in Europe, the US, South Africa, Israel, and really any place where the incidence was high enough.

And China and Russia are not "making big breakthroughs": just look at the vaccines again: BioNTech/Moderna/J&J/AZ all work extremely well, all things considered. The Russian and Chinese vaccines don't. Just ask/look at the charts of Chile. Or any Russian.