From the rebuttal you linked:
I am sometimes questioned by well-meaning but confused scientists who do not understand the role that scientific skepticism plays in society. Isn’t science itself enough? Aren’t all scientists skeptical, or at least they should be?
The author is not acting as a scientist when he consults on demonic possession. He's acting as a healer. Primum non nocere on this one is "are there any psychiatric treatments that will help the patient?" There may not be. If the patient is Catholic, living in a Catholic environment, a Catholic treatment may be the most effective course of action.
Further, the author is putting forth his anecdotes as anecdotes and his beliefs as beliefs. He has not convinced me in the reality of demonic possession. He has, however, convinced me of his belief in demonic possession, which is of greater pragmatic value in the solution-space of "devout Catholics whose loved ones think they're possessed".
I have always thought that, if requested to help a tortured person, a physician should not arbitrarily refuse to get involved. Those who dismiss these cases unwittingly prevent patients from receiving the help they desperately require, either by failing to recommend them for psychiatric treatment (which most clearly need) or by not informing their spiritual ministers that something beyond a mental or other illness seems to be the issue. For any person of science or faith, it should be impossible to turn one’s back on a tormented soul.
A quote of yours, if I may:
Saying 'I don't know, gotta be the devil tho' is essentially an evil act because it is thought terminating.
I think that's unnecessarily dismissive. He's not saying "I don't know, gotta be the devil tho." He's saying "I've ruled out everything but the devil." A secular psychiatrist would probably not make that statement. She would probably blitz right through Beelzebub and move on to whatever else looked promising. But the thing is, clinical trials and useful effects in the field don't overlap all that great, particularly when it comes to psychoactives.
Here's the question: is there potential harm from a religious ritual? I'm trusting that a clinically-trained psychiatrist does not condone exorcism rituals that have the potential to make things psychiatrically worse but that's trust, not knowledge. If my trust is well-placed, is there any harm from shaking a bible at a crazy person?