The multiplicative Merino–Welsh conjecture for matroids

Let $M$ be a matroid with no loops or isthmuses, and let $T(M;x,y)$ denote its Tutte polynomial. Multiplicative Merino–Welsh conjecture.

$$T(M;0,2)T(M;2,0)\geq T(M;1,1)^2.$$

This is presented as a seemingly stronger consequence of the additive Merino–Welsh conjecture, using direct sums and duality. Its status is not resolved in the supplied source.