The basis of Common Law extends back well before the advent of reasonable science, and it is entirely based upon belief of the assembled. In U.S. laws, that can be a judge, a panel of experts or judges, or a jury of the peers of the accused. But there is never a case in which material evidence itself is more important than who believes it, and how convinced they claim to be.
We know, from studies of memory and perception, that this is not a reliable standard of evidence from a scientific point of view. We know how memory is rendered harder to retrieve by stress, how our degree of certainty is unrelated to the actual evidence, how memory can be manipulated by the order in which its aspects are later recalled, etc.
But we try to adjust for this with redundancy. We try to make the jury large enough that someone on it will not we swayed by these manipulations, and we generally required unanimity. When there is not a panel or jury, we use the thread of appeal to ensure that a manipulated judge is questioned by more rational authorities above him.
Since statistics matured, science has an objective reference for when one ought to believe, instead of relying directly upon the ability to convince. But that standard arises later than most of the science we were taught in school. So, to some degree, the science you are used to was equally subject to the personalities involved and their political ambitions. But it has survived centuries of repeated attempts to disprove it.