Not knowing anything about the praxis of SBM, I presume that "prior beliefs and evidence" would be in the nature of noticing that people once used aspen bark tea to treat pain and fever, then determining through a series of experiments the exact molecule or group of molecules that produced the effect. At the end of the experiments, you determine that acetylsalicylic acid, ingested orally, is an effective remedy for pain and fever, with side effects stomach irritation etc.
I also presume that there is a more important aspect. If society believes that homeopathy works and that vaccines cause autism, that would be good cause to conduct very rigorous, credible (and above all media-friendly) experiments testing those beliefs.
If society believes that eating too many eggs is bad for you, test it. If we believe drinking red wine is good for you, test it. If we believe reptilian aliens are using sodium fluoride in the water supply as an adjuvant for their mind control rays, test it.
I presume, without knowing, that this particular aspect of SBM is very much about countering all the junk science hucksters stowing away on the gravy train, just because no one bothers to grab their freeloading asses and throw them off. So when Dr. Selschupplementsondeside (who may or may not be inspired by an actual person) touts a miracle cure on his cable television show, you put that on your list for potential testing and start tracking the hype versus scientific credibility ratio. If too many people start believing without knowing, you need some experimental results.
We can't test everything, so focus on testing the unanswered questions. Test the home remedies and traditional cures. Debunk the junk science.