To further this point, the Ultimania has Vayne's age listed at about 27, while Vaan's is clearly stated as 17. The story places emphasis that Penelo and Vaan knew each other as children and goes so far as to have a picture of the two as kids on the streets of Rabanastre

Ffxii_39_130.jpg

There is no real evidence to suggest Vaan or Reks have amnesia, or some magical force that made them somehow not age since that is an ability that only the Occurians and the dead have. There is no evidence to suggest that Reks or Vaan are Occurians or dead, so lets not go there...

The game and Ultimania directly tells you that Vaan and Reks parents (I would like to point out that it refers to both of them) died from the plague while Vaan was a 12 years old. Reks and Penelo's family took care of Vaan until Reks joined the military and Penelo's parent died as well. Vayne and Larsa's father is alive and well until about halfway through the game.

Your theory contradicts the Ultimania.