The question is about what is being done in the calculation of body fat. The procedure.
The goal of the procedure is to determine body density. To calculate body density you need to know the volume and the weight.
Now you can quibble about weight vs mass, but for medical purposes, weight is generally measured by a scale. I've been weighed in a numer of doctor's offices, and the technology varies, but none have immersed me in water.
But the only easy and cheap way to measure body volume is by total immersion. It makes no difference how massive or dense a body is. Once it is totally immersed you have its volume. But weight is a separate and independent measurement.
Try to look at what is being done. You want body fat. There is some empirically derived formula for estimating body fat from density, so you want density.
Density is a ratio of volume to mass or weight, so you need both volume and weight. You get weight with a scale. You get volume by immersion.
And yes, you could do a combined procedure whereby you measure floating displacement and total displacement.
If a body or object floats in the liquid, it also is a quick and easy method of determining mass. It will only work for mass if the object floats, meaning that the object is less dense than water. Every human body that I am familiar with is less dense than water. Ergo the water displaced by the floating body exactly equals its mass/weight. Force total immersion then the water displaced by the immersed body exactly equals it's volume.