There's a unicorn behind you. Yup, it's right behind you, but it's really quiet.
Oh, you turned around and it wasn't there?
Well it's an invisible unicorn.
And it's intangible.
In fact, no scientific test could ever verify it's existence.
But it's there, right behind you.
That's the false logic of believing in something just because it hasn't been disproved. If you claim something exists, the burden of proof is on you, the believer. If logic allowed for a burden of disproof, we'd have to believe in monsters, every religious deity, and magic, since I can't prove they don't exist. Should I just believe that everything exists? Nope, that's the fallacy of a burden of disproof. There is a reasonable burden of disproof, but it's to disprove the evidence for another's claims, not to disprove another's claims without evidence. There is no rational thought without a burden of proof behind every statement; you have to be able to back up what you say, or it's meaningless.
The problem with supernatural activity is not that scientists just don't examine the evidence of supernatural stuff, the problem is that they do. After almost 200 years of research, there is still no convincing evidence for any forces other than the 4 principle forces that we know of and the variations and/or interactions between them. This article,
Telekinesis and Quantum Field Theory | Sean Carroll , shows a chart that proves that there is no room for a new, supernatural, force of nature. This is my proof for my statement. If you still believe that supernatural forces exist, you can disprove me.