He’s truthful, in a sense.
Work Step by Step
The amount of buoyant force exerted on your large lead-filled preserver is indeed greater than the amount of buoyant force on your friends' smaller life preservers, because your life preserver displaces more water. However, the buoyant force on the preserver is much less than the weight of the lead-filled preserver, so the preserver would bring you down. We don't recommend using it.