What event transpired can't be changed but perceptions can change.
An individual can't state and be factual that they saw a demon, because not everyone shares the love of cheese. In truth what does that statement even mean, "I saw a demon"? That isn't a description it's a conclusion.
In my opinion, if someone believes they are haunted and are having SP the fear and the stigma that comes from some rigid belief systems will assure that they remain in agony for years instead of looking into several options. It's what scowl wrote about.
A person has an event that impacts their life and they become convinced that the conclusion they've reached (through their belief and talking with others who've shared a similar experience/belief) is the answer. Now if it is a one time episode (saw a ghost of their dead cat) it may not be a problem but if it is a series of episodes/events they may begin to obsess and fixate on that because they've become convinced and will not be moved to even consider alternative answers/explanations. This goes back to and is the fear of the unknown.This fixation will also give them a distraction from understanding the root of the stress or what started the SP cycles in the first place because a lot of people don't want to admit that they are having other issues. The person may have been experiencing one or more of the following; prolonged stress, lack of quality sleep or interrupted sleep, waking hallucinations, irritability and mood swings. So far this does sound demonic in nature. If they become convinced that's what it is by talking with others who have shared a similar experience how does belief really help? Does it reduce the stress, help them get back on a healthy sleep cycle, address mood swings etc and they BELIEVED with all their might that (prayer, burning sage, salt holy water, exorcism, fill in the blank) would work and their deity would deliver them. So they continue on in an unhealthy state rather than admit they didn't know and look at other possibilities. This doesn't have to shake the foundational belief system of the person. You can still believe in X and have SP. It's just that what they thought/believed/identified it as originally was.... dare I say it..... wrong. It's not about the whole belief system but the episode/event was misidentified.