One side says, "I remember this thing from when I was 1 year old".

Another says, "You cannot remember it, you must have reconstructed it from being told or from pictures."

The memory itself can certainly be falsified: if you remember your mom using an iPhone in 1998, then that memory is false. If you remember talking to your uncle but he died before you were born, the memory is false.

How do we know if the origin of the "memory" is the person's actual experience, or their imagination of it based on descriptions or pictures?

Well if it's an event that had pictures taken of it, if it's the kind of event which grown-ups talk about, then the simplest explanation is that it was reconstructed.

But my son, almost 5, is always coming out with random things that happened when he was 1 or 2, which are absolutely of no importance to us, and which we would have forgotten long ago if he didn't keep remembering them. Once, for example, my wife put a pair of his shoes on top of the car while she put him in the car seat, forgot they were there, and drove off -- obviously at some point they fell of and were completely lost. Every six months or so my son talks about that incident completely unprompted -- something of absolutely no significance to us, but obviously something that struck him. And about the time I lost my temper and sprayed him in the face with water -- definitely not a memory I'm eager to revisit and bring up.

Someone dogmatic person may still say, "You must be bringing that up yourself somehow." That is certainly an unfalsifiable assertion -- there's no way, other than my assertion and probability, to prove that I'm haven't talking about those shoes on a regular basis. But I think any person with an open mind is likely to agree that "he's remembering them" is a more likely scenario than "the grownups are talking about those lost shoes all the time".

Probably these "revisitations" are his brain's way of refreshing the memory as his brain grows, which probably means the memory as they exist in his brain will have been shifted over the years. But that's still an original memory -- that's how adult memories work as well.

If at any point he misses a "refresh", they'll probably be gone; but the memories he manages to do this for will probably stay with him into adulthood. If at any point he "misses" a refresh, they'll probably be gone forever.

The flip side of this, of course, is that many of the memories we think we have as adults are heavily edited too. A few years ago someone recounted to me an emotional conversation that they'd had with someone on their deathbed (as an adult, only a few years prior to that). As it happens, I was in the other room when this conversation happened, and my memory of that conversation was significantly different. Obviously at least one of us is "remembering" something untrue. As I had little "skin in the game" about the content of the conversation, and the memory this person has seems to me very consistent with this person's narrative about their life, I'm inclined to think my memory is more accurate. But who can tell.

This matches my experience also. Kids can "juggle" some of these extremely early memories into more permanent memories but the vast majority are dropped. It's only because of the early and possible frequent recall that the memories end up winning their mythic permanence.