"If you aren't basing your beliefs in facts, then what ARE you basing them on. If a fact cannot be checked, then how do you know it's a fact?"
I mostly agree, but I'd substitute "conclusions" for "facts" because the word "fact" sounds so final.
Even given this, it is not just the evidence that one bases their beliefs on, it is often other beliefs, such as the belief on
how evidence should be evaluated. All data is evidence, but evidence of what? Depends on how you interpret it. For example, ask a Christian what evidence there is of God and they may say something like, "Just look at a tree! How could that be without God?" Well, there is no doubt that a tree is evidence of
something (many many things actually), but is it evidence of God? It depends on how you interpret that evidence.
And what is the best way to evaluate evidence and reach a conclusion? Some people say, "It is what you feel in your heart", which is utter BS if you ask me, but that is still their belief and it would satisfy the definition of evidentialism, as it is given above. Objective, verifiable and (if possible) repeatable evaluation of evidence is what I prefer, because that is what I find leads to the most reliable conclusions which have predictive value.
In short, the term "evidentialsm" is not very useful because unless it also includes skepticism and the scientific method for evaluation of evidence, the mere
existence of evidence is insufficient on which to base beliefs.