What I don't understand is how that is possible without swallowing loads of water?:blackeye
Presuming there's no air/gas in the stomach (from food digesting),
the larynx-lungs valve is closed during apnea drinking and sword swallowing...
the pharynx-esophagous-stomach valve is open (allowing both water and sword), but little water will enter (because no air displacement, unlike the lungs).
I'd think not more than a few tablespoons of water would enter the stomach. (Though that's just a guess)
Swallowing is dependent on the tongue muscles pushing food/water/sword down.