Can you base an assertion or a belief on the fact that the opposing argument or arguments does not have clear evidence to support it, and that fact alone (DETAILS FOLLOW)?

Sometimes, we state a thing as fact or as our belief when we don’t have clear evidence to support it. The only thing we have is evidence that shows, we believe, that the arguments on the other side of the issue don’t have anything clearly supporting them.

In many ways, this is what our criminal justice system is based on…the fact that we’re innocent until proven guilty. When the jury comes back with a “not guilty” verdict, it is (or should be) a statement that the state did not present evidence showing clear guilt. In essence, they are saying “We find that the defendant is not guilty because there is not enough (or no) evidence that he is guilty.”

Do people find this applicable in other situations, or types of arguments, in their lives? If so, how strongly should we support or hold these beliefs? Further, can such a thing ever be an assertion (meaning that it is accepted as fact that something is true solely because there is no supporting evidence of the contrary)?