One semantic issue is the idea of "rejecting" statements. If a statement has no evidence either for it, or against it, we can "reject" it. But that's not the same thing as saying it isn't true (which is accepting the negation). By rejecting an unprovable statement we reject both the positive and negative.
Ah, and if we DO discuss statement impacting reality?
A: There is a rock coming your way from behind.
B: moving left dodges the rock.
C: There is no rock.
No evidences. Dodge?
But that's not really an impartial question.
At any time we have the possibility that a rock may or may not be flying at our heads from behind. So do we constantly dodge our head just in case? Of course we don't, due to the low likelihood of this being the case. We couldn't function if constantly dodging imaginary rocks. Because, by itself, the rock-coming-at-you scenario is highly unlikely: the type of thing that you can go years without occuring. Going by game theory, dodging constantly costs more than the rock damage x probablity.
Ok, let's say for argument's sake that you know that it's equally likely that the rock is there or not (50/50 chance, i.e. no evidence for, or against). In that situation, you dodge, since the cost of not-dodging vastly outweighs the cost of dodging. So if it's completely undecidable in probability terms, you should avoid the most-costly path for sure, which is basic game theory.
If, however, someone tells you "lookout! rock coming at your head!" we can ascertain more information about the probability. Either the person is a liar or they're truthful. Only a pathological liar would make this sort of statement with any frequency. So either you have knowledge of the person, or not. Since most people don't make up this sort of lie, then you'd assume they were truthful. However, if this was a person you knew with a high frequency of yanking your chain, then you'd probably not dodge.