Demonic activity. Probably hard to dismiss because those testifying have come to believe that demonic activity is the only explanation, and thus there's no way for them to describe the events that isn't shaped by that conviction.
I'll give some first hand testimony of an experience. A long time ago, in a city far, far away (New York), I got heavily into Crowley and the Ordo Templis Orientis. Working with his Magick: Theory and Practice, I attempted a ritual. The preparation involved a period of fasting, and not sleeping. It all went pear-shaped, and I awoke to find myself in my apartment amidst considerable havoc.
My instinct was to think that I'd somehow invoked something otherly, and it was responsible for the damage around me. I knew Crowley had a penchant for laying traps in his rites for those not properly trained. For some years afterwards I suffered from a particular kind of night terror: as I was falling asleep, but while still conscious, I would become paralyzed and then feel like I was plummeting downwards. This would generally be accompanied by aural hallucinations, the sound of something bellowing in a language that couldn't be human. Sometimes visual hallucinations, if my eyes were open. I thought that maybe the door I'd opened in the rite hadn't properly closed, and that I was almost within the reach of a 'demon'.
It was, of course, bollocks. The chaos I'd awoken to had been made by me. The first violent seizure, in a run of a decade of intermittent violent seizures, but the only one where nobody was around. I lived with that worry of demonic possession for a few years, until an enlightened soul from New Zealand (the first person I'd spoken to about the sleep paralysis) correctly identified it as a form of narcolepsy. I've had scans, etc., since. My brain is wired wrong, or maybe just differently. If I don't take care of myself physically, then it goes a bit haywire, and I'll have a seizure. The narcolepsy is haphazard, there's no way of predicting it, and there's no way of preventing. I have a bunch of other sleep related issues, the main one being insomnia, but it makes life difficult for the wife - I convulse when I sleep, and my limbs do not lie still.
My point being, an explanation of 'demonic' interference seemed rational enough, at the time. But it's just biology. I'm weird, but so are lots of other people. Enough for the science to have names for my various weirdnesses.