Vassiliev's stabilization conjecture for finite-type invariants

Let $K$ be a knot, and let a Vassiliev (finite-type) invariant mean any finite-type invariant of knots. Vassiliev's stabilization conjecture. If every Vassiliev invariant of $K$ is identical to its value on the trivial knot, then $K$ is unknotted.

This is presented as the simplest case of Vassiliev's stabilization conjecture and is anticipated as a consequence of the volume conjecture. The source does not provide a resolution, so the claim remains open here.