I could easily respond with
You don't drown from staying there, you drown from having too much water in your lungs.
You're just overcomplicating it. Yes, it's obvious that you don't drown as soon as you fall in a lake, but falling in a lake implies that you were not expecting it, therefore the shock might immobilize you or disorient you, making you that much more prone to drowning. However, if you think clearly while stressed or under pressure, you wouldn't drown at all. You'd swim out of there immediately.
Your statement is true, but is it really necessary?