@neologist,
I believe there is so much evidence out there, and so much uncertainty too, that the only way to be coming from a truly evidence based perspective is to be a scholar in the subject at hand. This is obviously not possible for the majority of subjects, since scholarship necessitates that we devote our time with fidelity to only a few subjects, and usually only one broad one.
This is part of my frustration with the "where's your evidence?" objection in informal dialogue. The fact is we trust certain sources over others and rely on other heuristics like reputation of the institution or individual proponent, and whether the information being put forward is psychologically pleasing to us or not.
"Where's your evidence?" should be "What's your evidence?" And we should interrogate why you credit that evidence over other kinds, and by evaluating one's reasons some further understanding might be reached.