You're wrong, and here's why:

The Spartan children were kidnapped and when they were they were immediately replaced with something called a "flash clone" due to the problems of cloning a full size human in the game-universe all of the children would die soon of various diseases and the parents wouldn't ask any questions.

Plus at the end of Halo 3, Cortana says It's been an honor serving with you, John. She says goodbye in Halo 4.