I'm the person who, over 18 years ago, originally came up with the alternate theory of the film arguing that the creatures in the narrative were actually demons instead of aliens.

I wrote this for The AV Club, but someone made a Reddit re-post of it which got thousands of hits --which is how Reddit first came to my attention, prompting me to sign-up here. Since I originally wrote this, it's been quoted and re-posted in publications around the world many hundreds of times --and I still stand by the analysis (if not my shabby writing):

HERE'S WHAT I ORIGINALLY WROTE:

Let’s skip the M. Night hatred for a moment. I, too, think he’s become something of a joke. But he has made a number of worthwhile movies, and this is one I initially couldn’t stand, thinking it was full of ridiculous plot-holes. And then…EUREKA!

When I first saw this film, I didn’t realize that it wasn’t about aliens at all. It’s about the return of demons.

Notice it’s all about a priest’s resurgence of belief, and a preordained moment of redemption-if-dared-and-attempted. There is no alien technology or weaponry or clothing of any kind, only a clawed, naked beast-creature and lights in the sky (which are just like Biblical images of Heavenly Lights).

Furthermore: The running joke throughout the movie is that people see these “invaders” in a way that’s related to their particular frame of mind: The cop sees them as prankster kids, the bookstore owners see them as “a hoax to sell commercials,” the Army Recruitment Officer sees them as invading military, the kids see them as UFOs…and the priest sees them as test of faith.

This understanding of the film removed my hatred of the “You’ve got to be kidding me, they were killed by WATER!” concept. In fact, the priest’s daughter had been referred to as “holy” (as revealed during Mel’s key monologue) –-recognized, he stated, by all who saw her at her birth as “an Angel.” And her quite particular relationship to water is shown to be very special and spiritual: In other words, she has placed vials of what are, essentially, HOLY WATER all around the house. (And the creature’s reaction when coming in contact with this blessed liquid is exactly like monsters/vampires being splashed by spiritual “acid.”)

This view of the movie also explains the creature’s actions: They act like superior tricksters, are not able to break in through closed doors, can be trapped behind simple wooden latches –all mythological elements of demons and vampire-like creatures of lore. It also (and this is most crucial "proof") explains the news over the radio at the end of the movie that an ancient method of killing the creatures has been found “in three small cities in the Middle East” –-which one would suspect are likely the religious “hubs” of the three main Abrahamic traditions, each discovering the “mystic methods” of protection-and-dispatch that I’ve noted earlier.

Note also: All the Christian iconography throughout the movie, the references to “Signs and Wonders” (the true meaning of the title), the crucifix shapes hinted-at everywhere (check out the overhead shot, looking down on the street driving into town) and the ultimate fact that the entire movie is built around a Priest rediscovering he is not abandoned to a random, Godless, scientifically-oriented Universe but, rather, is part of a predicted and dreamed-of plan.

Now, these creatures may for all intents and purposes be some sort of extraterrestrial or inter-dimensional “aliens.” But the point of the movie seems to be that they are, in the ACTUALITY OF THE FILM'S WORLD, the dark stuff from which all the character’s tales of devils and night-creatures were born.