Dr. Jim Tucker and Dr. Ian Stevenson from the University of Virginia School of Medicine have done research on the topic and have published books detailing the accounts of many children who claim to remember "previous lives".
Here are some examples of the literature on the subject:
The evidence, as far as I can tell, is largely anecdotal and it seems the majority of cases originate from Eastern societies where belief in reincarnation is common, which could be indication for some sort of cultural cause.
From Where Reincarnation and Biology Intersect:
Children who claim to remember a previous life have been found in most
countries where they have been sought. Reports of such children occur
frequently in countries and cultures in which the belief in
reincarnation is strong: the Hindu and Buddhist countries of south
Asia, the Shiite people of Lebanon and Turkey, the tribes of West
Africa, and the tribes of northwestern North America.
There is no accepted explanation for this phenomenon. Dr Tucker has suggested reincarnation through quantum mechanics.
Carl Sagan in his "The Demon Haunted World" states that this is one area that needs more research, not because he thinks reincarnation will be proven true, but because they are hypothesis that could be true, aka they have some level of experimental support.
It could also be false memories. Introducing false memories is fairly easy; there have been studies where the subjects were told that they did something embarrassing or illegal when they were young kids and asked if they remembered it. Then they were given some details in an authoritative manner (We talked to your mom, she told us all about it...) and then a significant number of participants started remembering something that never happened. This could happen unintentionally as well, for example by the parents discussing the birth marks that the child overheard. This is speculation of course.
So in conclusion, there have been many such documented cases. It's not clear what's causing it and if it's "real", therefore there is no way to know if that particular case the child is remembering his previous life. The case described in the article fits the pattern of other reported cases so it seems plausible that some of it happens, but it likely got exaggerated over the years.