I've thought about this a lot and I have an idea but don't know if its even medically feasible but here goes.
I think there is at least a slight possibility that little shards of memory somehow find their way into our DNA and get passed down to subsequent generations. Not specific memories but ones from the deeper layers of consciousness that either lay undisturbed for long periods of time or very powerful ones that the mind through hypothetical mechanisms decides is important enough to encode in our DNA.
DNA has plenty of room for this extra information that hypothetically finds its way into the deeper recesses of our memory. Also, there is a precedent for inherited memory in the animal kingdom. Baby chicks respond very viscerally to a shadow of a chicken hawk when the shadow moves towards them from the front but show no reaction when it "flies" over their head from behind. Behaviour might be instinctual but a reaction to a specific stimulus has to be at least partially pre-learned which begins to suggest a mechanism for encoding and transferring learned behaviors.
I don't think any of us have led prior lives but I can't rule out the possibility that there are little bits and peices of our ancestor's memory floating, unanchored in our brain such that when a "live" experience, on its way to being stored, brushes up against one of these floating, uncataloged engrams which conceivably could trigger a "recollection" that didn't actually occur. Not to us, anyway but maybe to someone in our geneological treehouse.
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