Good point about surveillance cams. But perhaps the Extraterrestrials deactivate those the same way they shut off cars in transit and so on?
Remember, unlike lightning and similar natural phenomena, we are dealing with an intelligent and technologically highly advanced species (assuming there's anything to the extraterrestrial angle).
And as for investigating these cases as psychological phenomena I would assume that the late Dr. John Mack and the other psychologists/psychiatrists who have so far dealt with abductees would have BEGUN from that angle and only been forced by what they found to be convincing evidence to admit that the abductions were (at least in SOME cases) actually occurring.
Dr. Mack is on record as saying "When I first encountered this phenomenon, or particularly even before I had actually seen the people themselves, I had very little place in my mind to take this seriously. I, like most of us, were raised to believe that if we were going to discover other intelligence, we'd do it through radio waves or through signals or something of that kind.
"The idea that we could be reached by some other kind of being, creature, intelligence that could actually enter our world and have physical effects as well as emotional effects, was simply not part of the world view that I had been raised in. So that I came very reluctantly to the conclusion that this was a true mystery. In other words, that I—I did everything I could to rule out other sources, or sexual abuse. Some of these people are abused. But they're able to tell, distinguish clearly the abduction trauma from other forms of abuse. Some forms of psychosis or people making up stories—I could reject that on the basis that there was no gain in this for the vast majority of these people.
"I've now worked with over a hundred experiencers intensively. Which involves an initial two-hour or so screening interview before I do anything else. And in case after case after case, I've been impressed with the consistency of the story, the sincerity with which people tell their stories, the power of feelings connected with this, the self-doubt—all the appropriate responses that these people have to their experiences.
"People, in fact, have been observed to be missing at the time that they are reporting their abduction experiences. They return from their experiences with cuts, ulcers on their bodies, triangular lesions, which follow the distribution of the experiences that they recover, of what was done to them in the craft by the surgical-like activity of these beings. "
---John Mack, Interview on Nova
You can read the rest of that interview here: http://www.pbs.org/wgbh/nova/aliens/johnmack.html