This is a urban legend. Not sure if it was true at any point, but it is not the case.
Chickens were selectively bred to grow fast enough as it is, to the point that some breeds have a percentage of offspring lost. Try to make them grow any faster and more will die.
> - Higher quality meat (Chicken gets more exercise and movement, as well as increased quality of feed)
At least for cows (and most game), you don't want them to exercise too much or the meat won't be as tender. Is it different for chickens?