Sorry. I must have missed the post where you presented this issue.
So we're dealing with the
likelihood of truth. Okay, but first of all, lets do away with all the bias and irrelevancies and properly phrase your "disagreement."
1) An isolated observational fact has a greater likelihood of being true
than
2) A set of observational facts that are connected in a predictive and explanatorily powerful theory
Because the strength of the set of facts is predicated on what it does rather than what it is, one first has to show why a theory would necessarily lend strength to the truth of the set of facts. Honestly, because a theory is a tenuous interpretation, which admits to revision, I fail to see how it might impact the truthfulness of a set of facts at all. And even if one does feel "what it is" is a salient determinant it would have to be shown why the connectedness of the facts itself impacts the truthfulness of the set. So, I'm going with number 1. And individual fact has a better chance of being true than does a set of facts. Kind of a parsimony thing as well.
While the relationship of various facts may be contentious, by its very definition, "fact" admits no quarrel. Want to question and attack the basis of a fact? Go right ahead, but unless one can show that the indisputiability of a fact is flawed or significantly unsound there is no reason to dethrone its assertion from its status as fact. One is perforced required to accept it as 'confirmed to such a degree that it would be perverse to withhold provisional assent." (Stephen Jay Gould's definition.) So any quarreling going on would be over the particulars that
happen to support a fact, and not the fact itself.
.