If we assume that the probability of a witness testifying to an event is higher if the event actually happened (a reasonable assumption), then it is true that observing that testimony makes the event more likely. How much more likely it makes it depends on how likely the testimony is in the absence of the event. And of course, if the prior probability is low enough, the increase might not be enough to make it likely (e.g., if the witnesses make the event 1000x more likely, but the prior probability is 0.000042, it's still a pretty safe bet that it didn't happen.)
Multiple independent witnesses might help overcome those sort of bad prior odds: they increase the probability very rapidly as you add witnesses. But this requires that they be genuinely independent not only of each other, but also of any confounding variables that might result in a false observation of the event. And that's the real catch, because a lot of potential confounding factors wouldn't be unique to a given witness.
Consider a less controversial example: UFO sightings. If 100 witnesses say they saw a UFO, that might seem convincing...but if it turns out that the first witness actually saw Venus, the rest of the sightings suddenly become a lot less convincing; the witnesses weren't actually independent, because they were looking at the same night sky and were exposed to the same confounding variable. It's not enough to ask how likely they are to report an alien spaceship given that they actually saw one (P(report|event)). You have to also ask, "What else might have caused them to make that report?" (P(report) = P(report|event)*P(event) + P(report|~event)*(~event)). And it can be really hard to rule out all other potential causes.
