The only drown proofing I had ever had explained to me was from a Navy diver. He described it that you have their hands bound behind their back and their feet bound. They then exhale and sink to the bottom and push off the bottom, repeat. I'm not 100% sure how that drown proofs someone, but that was my understanding.
You were taught incorrectly. Have a look at Drownproofing for the history and explanation of how to do it properly.
Essentially, image taking a full breath and letting your body go limp in the water. Your lungs will make the back of your head and your back float to the surface. When you feel you need a new breath, exhale and pop your head up so your nose and mouth are out of the water. Quickly take a breath before you slip below the surface. Go limp again and you should float to the surface with the back of your head and your back on the surface. Keep doing this. For most the time you are just floating limp in the water and expending no energy. In theory, you should be able to do this indefinitely.
This technique will prevent you from drowning but because you are not curled up, you will be losing heat from arm pits, crotch, etc. and still have to worry about hypothermia.
It is odd because the Navy did adapt this technique. I think somewhere along the line someone misunderstood how the technique worked.