Flag-geometric characteristic polynomial conjecture for two-step matroid flags

Let $M$ be a loopless matroid of rank $r$ on $n$ elements, and let $U_{1,n} \twoheadleftarrow M$ be the corresponding valid matroid quotient. Define the flag-geometric characteristic polynomial by

$$K\chi_{(U_{1,n},M)}(q).$$

Flag-geometric characteristic polynomial conjecture. One has

$$K\chi_{(U_{1,n},M)}(q)=(q-1)^r.$$

This conjecture concerns whether the flag-geometric characteristic polynomial of a two-step flag matroid can distinguish the flag matroid; the stated formula suggests that it contains little information in this case and is supported by computer computations.