This is a myth! While sitting too close to the TV might cause eyestrain, no damage is done to your eyes. Many parents grow concerned when their kids sit too close to the the TV. Because children are able to focus very well at close distances, they don't experience much/if any eyestrain compared to adults.
However, it should be noted that some children might sit too close because they are near-sighted and need glasses! If you're concerned, schedule an eye exam for your child today.