This question assumes the existence of laws of nature. As I recognize that this premise may be controversial to some extent, frame-challenging answers are welcome. However, please note that there are already questions entertaining this possibility: Are there laws of Nature?, Is it possible that the laws of nature don't exist?.
With that said, let us suppose that laws of nature do exist and that a scientific consensus has been reached regarding certain heavily tested ones. Now, consider a scenario where person P is well aware of these established facts. Would it ever be reasonable for P to conclude that one or more of these rigorously tested laws of nature were violated solely on the basis of testimonies?
To clarify, P does not have direct access to technology, measurement devices, camera recordings, or other forms of physical evidence related to the alleged violation. The only evidence available to P in this thought experiment consists of testimonies—writings, speech, or reports produced by other individuals. These testimonies may vary in nature; for instance, they could originate from a single individual or from multiple people claiming to have witnessed the event. The witnesses might be alive and available for interviews, or they might no longer be alive, with their testimonies preserved through a tradition that values their accounts (as in the case of alleged "miracles" deeply valued by certain religious traditions).
The question is: under what conditions, if any, could testimonies alone reasonably lead P to conclude that a violation of the laws of nature occurred as a matter of fact? Or is this the type of conclusion that testimonies, regardless of their nature or number, could never justify?