This is true, but drinking two liters of milk is a lot less dangerous than drinking two liters of water, because that much water at once will throw your electrolyte balance off, and that's what can kill you. Milk has electrolytes in it so the effect isn't necessarily as dire. But... still wouldn't recommend it.

Dude when I'm running a race I have to walk while drinking the tiny little paper cup of water they give you enroute because the physical activity combined with drinking something makes my stomach churn (nerves might also be playing a factor since I'm still at the stage where every race I'm excited but also too nervous to eat and struggle to get enough calories in before the race)

I know. I have seen videos from like 2010 of people puking after trying that. Although 2L is still quite a bit less than a gallon.