Oh, please. She's making a huge generalization. Maybe her own kids can't drink milk before exercise but that does not apply to everyone else, or anyone else at all. Everyone's different.
Gatorade? Our pediatrician is against it. She says that the whole "it has electrolytes and kids need them during sports" thing is simply untrue. Replacing electrolytes is what you do when someone has been vomiting so much that their body chemistry is getting out of balance, or when someone -- like, say, an elite teen or adult athlete -- is exercising very hard in extreme conditions. It's not for kids running around the soccer field. The artificial colors alone throw some kids off, and the sugars and other chemicals are not healthy at all, while Gatorade has managed to convince parents that it's some kind of health drink and fine to drink by the gallon!
Water. Most kids in the U.S. are always at least slightly under-hydrated, at all times -- there was a recent report on that: A study published last year said that more than 2/3 of kids in this country are always somewhat dehydrated. Filling up on sugary (or fake-sugar-chemical) drinks like Gatorade tends to make kids feel full very fast so they don't drink enough of ANY fluids when they're gulping down Gatorade (or similar sports drinks).
Ask a pediatrician -- he or she will probably say to treat Gatorade like soda: Very little, period, and it's a treat, not a health supplement.