I think the first part you said here is the crux of the matter: can things be evidenced, even without having a scientific explanation ?
That depends on what you mean by "Evidenced"...
Typically, people mean that its scientifically explained. But I agree that you don't have to define it that way.
You apparently say no, but I think this is a misstep because there comes a point where you do have evidence that something happened, but still without scientific explanation.
Here, you'd have a
reason to believe something happened, but not actual "evidence" that it did happen.
Now I am not talking here about observed, repeatable phenomenons. The sun rising, or the universe apparently demanding some sort of dark matter. I agree that such things are to be put into the unknown folder.
However, I think this is a qualitative difference from what we see in the movie paranormal activity: these are evidenced (let's suppose that the video is genuine, ie not a hoax) yet are one time, unrepeatable events, and so still fall outside the realm of science.
Typically, people would not count that as actual evidence then. But yes, it would be a good reason for you to accept them.