Well, we need to clarify the difference between the file itself, and how you're viewing it. I have no doubt that your 16-bit file is as perfect and smooth as you'd expect it should be. But no matter whether your file is 16-bit, 20-bit, 100-bit, or even a thousand-bit, you're still only viewing it on your screen. And your screen, unless you've spent big money on one of those 10-bit jobs, is 8-bit at most. (Some older screens were even lower!).
I don't profess any great technical expertise in this matter. But my guess is that you're right, in a roundabout way, about the dither on the 8-bit file. The dither is helping your screen, as much as the file itself.
Does this seem plausible?