Nah! Think of a vein in cross section. Fat molecules are travelling down the vein and get transported (like in Star Trek) through the vein wall and deposited on the other side. Later, new fat molecules also get transported across the venous wall, but the transporter beam is only powerful...
That presupposes that fat is deposited from, say, the body cavity. What if it is instead (at least in part) deposited directly from the blood stream through a venous wall, and thus builds up from the bottom, not added to from the top?