>> Also maybe that when you looked through a hole the shaman/priest/ordinary person looked
>> into the otherworld or the future.

I would say that this is almost certainly true of tombs. I don't think that it is too great a leap to think that the same applies to holed stones in general. The healing of somebody by passing them through a hole moves them from one world to another leaving the illness behind. Maybe, when ill and close to death, a person was believed to be partially in the other world and so putting them through the hole brought them back into this.

Or perhaps the passing through the hole was a shaman's diagnosis method originally, like a Neolithic CAT Scan :-)