The only option for someone who wants to double check research is to completely replicate a study, which is quite a bit more expensive than double checking the researcher's work.
The organizations who fund the research are (finally) beginning to require it [0][1], and some journals encourage it, but a massive cultural shift is required and there will be growing pains.
You could also try emailing the corresponding authors. Any good-faith scientist should be happy to share what they have, assuming it's well organized/legible.
[0] https://new.nsf.gov/public-access [1] https://sharing.nih.gov/
Feels like wrong way round - organisations paying for journals should be demanding it as proof?
One of the purposes of a site on which I work (https://fairsharing.org) is to assist researchers in finding places where they might upload their data (usually to comply with publishers' requirements).