Interestingly UFOs and supernatural events have been clumped together, but afaik these UFO claims typically don't require rewriting the laws of physics. If a UFO's existence was proven, and in the public domain, it would go from -100 to +100 in terms of people's attitudes of "that's all just a bunch of balogna" to "of course, we have always known it is very unlikely we are alone." However, a supernatural event would fundamentally shake up our scientific understanding of the universe. I think they're completely different types of possibilities.