This doesn't make sense at all. The screener is a teammate of the ball handler. The guard is continually guarding the ball handler. There is no rule that would say the closely guarded situation has ceased, as long as the guard stays within 6 feet of the ball handler.

The case play is as close as anything in the case book gets to this play, and seems quite clear to me that screeners have no impact on the closely guarded count.

There is also an NFHS-produced training video that states, word for word, with an accompanying slow-motion video clip, that the closely-guarded count continues when the defender stays within the required distance of the ball-handler while going underneath the screen.