Gravity is the name that we give to a force that everyone experiences every day. Things fall when unsupported in a gravitational field. Mass has weight in a gravitational field. You don't have to believe in gravity for it to operate. Even if you don't believe in the existence of gravity, you would still be unwilling to step out of a 10th-floor window. Gravity is not an elusive theory that requires proof to validate it. Gravity is a natural phenomenon and there's a scientific theory that states some of its properties. Gravity is not "scientifically validated" because it is not something that requires proof. We live in a gravity well, all particles in the known universe experience the gravitational force, etc etc.
Is reincarnation real? Could be. Is there any proof that it is real? No, not really. However, it is an incredible claim. So the standards of the evidence will be commensurately high. If I claim that I have a cat for a pet, it is not such an incredible claim. I can post a picture of me and my cat on the internet.
But if I claim that I have a T-Rex for a pet, and post a picture of a T-Rex with me standing on its head, you would justifiably be skeptical of my claim.
Extraordinary claims require extraordinary evidence, as Sagan pointed out.
Just-so stories don't amount to evidence when it comes to extraordinary claims. If so-and-so said that he heard of a kid who was the reincarnation of some person who died some time ago, that is an extraordinary claim. Did it really happen or is he lying? What is more likely: that the man is lying or that the story is true.
Let me quote David Hume on this matter. "No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavors to establish."