Well, just to hammer in, you can't affect the consciousness mind without affecting the physical mind. Duality is a dead concept. If God can affect conciseness, he will do so by affecting the physical mind.
As for god being proven with statical anomaly, possibly. Though Science could only say there is an unknown force causing these neurological event.
The issue with God, as it has been brought up before, is that it lacks definition. It also lacks a scientific one. There no operational definition of god. It make it hard and impossible to claim actions are of god.
Until a falsifyable model of God can be presented, then Occam Razor tells us a natural explanation is still preferable as it has the least assumptions.
Well, as Phil Plait has stated, much better then I could, is that UFO are real, then those which are in the sky most often, or watching the sky should see most of them. These group of persons, aviationist, and astronomers (professional and amateur alike), are knowledgeable of the artifacts in the sky. Therefore they would recognized unknown objects more readily then a lay person.
What we do see, are a small fraction of aviationist, and astronomers reporting unknowns as aliens. Which are contradicting themselves. (I don't know what this is, there I know what it is.) This is expected. You'll get extreme in any group. But the majority aren't seeing aliens. Who do see aliens are those who are undereducated in astronomy, optics and the atmosphere. The group who are talking out of their asses. You'll see them make claims about speed, size, and height when they have no sense of scale. (This is of course speaking to just spotters, those claiming encounters of the third kind, have a different list of explanations). And most of these group never really gave serious thought to the UFO claim, or already believed that UFO visiting us was probable. They're more incline to say Aliens! Instead of 'Atmospheric Optical Refraction caused by difference in mostiture and density!'
And something very similar can be said of those who say they have experience god. They are the one more incline to think that God will do this, and the one undereducated in paradolia, and how the brian play tricks on itself. We do see supposed HARDCORE atheist (the one of celebrity, can't seem to demonstrate this fact) scientist becoming religious. Though honesty, most who claim a higher education are fucking liars. Such as Kent Hovid, so forth.