Spoken like a true INTJ. Love it.
As an INFJ, I don't need proof to believe. I have experienced things that completely defy explanation. Things that i knew without a doubt were about to happen, could not explain why and then did within less than a minute.
The way this woman explains herself is believable. I don't believe she is an INFJ nor do I believe she is a liar. I think she experienced something that was real to her and is trying to explain it the best way she can. I think she is sensory and probably extroverted. Most likely a feeler (so, who knows if the interpretation is a bit jaded), and probably a J based on the way she explains it. She broke it down into good parts that were understandable and clear. There are some things that can not be monitored and proved by data. I believe this is one of those things; at least until there is a technology that can give some visibility into the ether.
Or are you an atheist? No judgments, just curious.