Here are my initial thoughts. They are off the top of my head (as usual) so please feel free to pull them apart!
Firstly we need some broader background information. It is well known that we have what has been termed "an overactive agency detector" that often gives false positives due to its advantageousness with regard to survival. Simply put, if you see a shadow out of the corner of your eye and hear a rustle in the bushes then it is more advantageous that this gives rise to the sense that there is some agent causing the shadow and rustle and that this gives you the instinct to run. Even if your brain gets it wrong more often that not, this is much more advantageous for you in terms of survival because the alternative is that you would easy meat for a wannabe predator. People would just stand around thinking "Oh, that's nothing" whilst a predator was lining himself up for a meal! A consequence of this is that our brains do not cope at all well with coincidences, especially coincidences into which we read (or to which we can assign) strong meaning. So even if we mustn't rule out agency a priori, neither must we rule out the possibility of us falsely attributing agency in the face of coincidence. Even after his experience, this seems to be the type of open mindedness that the author is calling for.
When we look at this situation, we can see the leaps that the author's wife made over an extremely short period! A radio that had not been working, is found to mysteriously be working on the couple's wedding day. On discovering this, not only does the author's wife make the leap that this has been caused by an invisible agent, but by her Grandfather specifically. Thinking as broadly as possible, I can see why even some Christians would take issue with this. The Bible (particularly, the OT) strongly prohibits contacting the dead, states that the devil and demons can masquerade as angels of light, tell us what our itching ears want to hear and that we should test spirits! Even if it was an invisible and supernatural agent, how do we know it wasn't a demon attempting to lure this sceptical woman down a dark path? If she is now open to the possibility of her father trying to contact her, isn't she now more likely to contact a medium to see if she can make further contact with her father and see if she can communicate back and so on?
The woman obviously concluded (almost instantly) that it was her Grandfather because the instinctive and strong sense of agency she felt in light of the event was also coupled with very strong and positive feelings. But all of the above highlights why we can't just blindly trust these leaps and I'm speaking of someone who has had experiences similar to this (although, not on the same scale). The person who looks at a sunset and gets a strong sense that "someone must have made all this" and attributes it to something omnibenevolent simply because the feeling is positive is doing exactly the same as the woman in the article.
So yes, the experience is very similar to spiritual experiences of God and that is simultaneously a problem because we do have very good reasons, based on background understanding of how the mind works, to question the leaps that the woman made on entering the room and hearing the radio. On the basis of recent research, this type of agency detection is something that the right hemisphere of the brain seems to be responsible for. The right hemisphere is keeping an eye on outside broad concerns whilst the left hemisphere focusses on the detail (eg, eating the food). It is the right hemisphere that detects and agent and says to the left hemisphere "run!" if it detects something that is potentially dangerous. However, the right hemisphere is less precise for the reasons I've described. "Hearing God" (or any other spiritual being) is consistent with the left hemisphere mistaking a communication from the right hemisphere as contact from another agent.
