This is not correct at all. Some surplus protein is converted to sugars (glyconeogenesis), from there it has a good shot at being converted into triglycerides

This is not correct at all. Some surplus protein is converted to sugars (glyconeogenesis), from there it has a good shot at being converted into triglycerides and stored as fat. If it was as simple as raw physical storage, bodybuilding would be dominated by eating-contest winners.