"They don't have any evidence that this happened." That is what you are reading in the news as a defense to the assertions of sexual misconduct. What is meant is that the statement against me is not credible. Evidence in a court of law can take many forms. It might be writings, photographs, charts, or even ledgers from a business. It can include ancient documents and government records. But evidence also includes a statement of a witness.
The question with all these forms of evidence is whether or not they can be believed. Testimony under oath from a witness is evidence that may be just as convincing as a photograph, business form, or government record. The credibility of a witness is generally easier to attack than one of the other forms of evidence. It becomes harder to attack credibility when multiple women describe the same thing happening to them in the same pattern.
When you hear the next politician or media star claim there is no evidence against him realize there is evidence in the form of a statement but the claim is that the witness is not credible. Then you will have to ask yourself, as Groucho would say, "Who are you going to believe, me or your lying eyes?"