A fourth down strip sack fumble recovery would not be a turnover on downs. It would just be a turnover because the offense did not complete the play.
Provided the original offense recovers the ball, that is indeed a turnover on downs. How could it be possibly scored as a normal turnover if the original offense has the ball at the end?
A true turnover on downs does not allow the defense to advance the ball or score a touchdown.
A 20-yard tackle for loss (e.g. sack) on 4th down advances the ball for the defense and is a turnover on downs.