I tried to post this reply on Gary's blog but had some issue so I'm posting it here:
"This is all based on the assumption that the video wasn't doctored in any way."It would be a more interesting argument if your basic assumption was not flawed. Paranormal Activity is a work of fiction filmed in documentary style. It's not real.
Another problem is your understanding of atheism. The simplest way to define atheism is a lack of god belief. There are atheists who fall for all kinds of other hokum including ghosts and homeopathy. It is possible to believe in poltergeists, demons, unicorns, and leprechauns without subscribing to a particular religion or believing in a god.
What you may mean to ask is "How does a skeptic explain...?". Skeptics, generally speaking, are people who demand evidence of extraordinary claims before acceptance. Those extraordinary claims could pertain to just about anything including religion, apparitions, aliens, or werewolves. Atheism is much more specific. While there is quite a bit of overlap, skeptic and atheist are not synonymous. In my opinion, any sufficiently informed skeptic should be an atheist but there are those who disagree. People are shockingly good a partitioning parts of their brain to shield cherished beliefs from scrutiny.
Now that we have our terminology straight, let's get back to your question. How does a skeptic explain such a thing? To my knowledge, there hasn't been any evidence that defies conventional explanation or is strong enough to warrant it. Even if there was, the important thing to understand is that unexplainable evidence is only indicative of our ignorance. We don't know EVERYTHING yet and probably never will. As science and technology progress, the gaps in our knowledge grow smaller and smaller but there is still much outside of our grasp. When we try to fill those gaps with superstition, we only stand in the way of our own progress. Let's not forget that many medical conditions (esp. mental illness) were attributed to demonic possession until relatively recently in human history. I knew a Nigerian man who was firmly convinced that meteors were the souls of the deceased moving on to the afterlife. He was not interested in any explanations about space debris burning up as it passed through earth's atmosphere. His superstition stood between him and knowledge.
There is a compelling hypothesis in the physics world right now that suggests our universe might actually be part of a Multiverse. That is to say our known universe is one of 6, 13, or even an infinite number of parallel universes that may interact with each other in unknown ways. There may even be a copy of you in each of those universes leading a slightly different life. It's kind of a trippy concept to wrap your head around but the evidence is surprisingly strong. (read up on String Theory if the topic interests you)
Suppose we had an unadulterated video of what appeared to be an apparition walk into a kitchen and drink a cup of coffee and then vanish. A credulous individual may claim that this is clearly evidence of the existence of ghosts and/or an afterlife. What if the "apparition" was actually caused by a brief "window" into another parallel universe? Perhaps the coffee drinker saw the person holding the camera in the same way. Is my explanation any less likely? No. It may very well be wrong but at least it is based in reality and may some day be testable.
This is purely hypothetical but it illustrates my point. Unexplainable evidence does not justify appeals to the supernatural. That would be an intellectual dead end. Unexplainable evidence just reminds us that we have a lot more to learn. I am comfortable with the fact that I cannot explain everything and realize that greater understanding may come with time. I feel no need to insert my own cultural biases to fill the voids in my understanding. It is o.k. to say "I don't know".
Update: Gary fixed the comment issue on his blog so this can now be found there.