The planar surface conjecture for knot exteriors

Let $K$ be a knot and let $E(K)$ be its exterior. A non-meridional essential planar surface is an essential planar surface in $E(K)$ whose boundary slope is not the meridian.

Planar surface conjecture. A non-meridional essential planar surface in a knot exterior is either a disk or an annulus.

The source gives this as a strengthening associated with the cabling discussion; its general status is not resolved in the supplied text.