The Red Leaf Faction certainly belongs to the Three Teachings of Dayan and is collectively referred to, along with the Green Lotus Sect and the White Jade Gate, as the Green Lotus Red Leaf White Jade Sect.
Concealed within Dayan yet not revealed to the world, they manipulated mortals from the shadows, under the guise of ascension.
This has nothing to do with being clever; cultivation is all about one's perceptiveness and innate talent. Being clever is considered a lower grade quality.
It only relates to the Dharma Technique.
The Soundless Gate Sect required spirit and will; therefore, it directly partook in mortal affairs, with its Sect Leader even governing the Southern Plains.
And other sects were more or less the same, directly needing mortals, hence they straightforwardly became involved.
These Three Teachings were different; they didn't need to deal directly with mortals, so they could set up an intermediary layer.