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I'm sorry to tell you that there's countless real-world examples to counter your "basic physics." I shouldn't have to tell you that the real world is far more complicated than that. The theoretical math does not matter when we know for certain from example that people who cannot swim will drown when thrown into water.Humans are naturally buoyant. Its basic physics. The pressure from down below when higher then the pressure pushing down naturally pushes people upwards. Rather simple stuff. There are factors that offset this of course, such as weight, upper and lower body strength, cardio, density, respiration rate etc. Of course there are more extenuating circumstances such as the density and volume of the water, and of course the pressure pushing both upwards and downwards upon the person, but for the most part a relatively fit person should have no issue staying buoyant (as long as they don't flail around and waste energy).
So, yeah it is true.
If it was so easy for people to simply float, then so many people wouldn't drown. You have your false assumption baked into your argument right there: "(as long as they don't flail around and waste energy)". People who have zero experience swimming are not well-informed on how to safely stay afloat. They will make all of the mistakes which lead to people drowning.