No that is not true.

First of all to "pull" a fly underwater, the direction of the pull must be from under the water. In other words, the tippet and fly line must be sunk for this to happen so the direction of pull is down.

Secondly, a dry fly is most often fished "drag free" which means the tippet should not pull on the fly at all. No pull = can't pull down.

So wrong on both counts.