There are circumstances where X asserting A provides evidence against A (for not-A). Some speakers are less reliable than others and there is no necessary reason a speaker can’t be so unreliable that her claims provide zero evidence for or against what she asserts. Moreover, there is no reason a speaker can’t be anti-reliable. Perhaps she is a pathological liar. In this case her statements are inversely correlated with the truth and an assertion of A should be taken as evidence for not-A. As long as your math is right there is no reason for this to violate conservation of evidence.
There are circumstances where X asserting A provides evidence against A (for not-A). Some speakers are less reliable than others and there is no necessary reason a speaker can’t be so unreliable that her claims provide zero evidence for or against what she asserts. Moreover, there is no reason a speaker can’t be anti-reliable. Perhaps she is a pathological liar. In this case her statements are inversely correlated with the truth and an assertion of A should be taken as evidence for not-A. As long as your math is right there is no reason for this to violate conservation of evidence.