Let $G=(V,E)$ be an oriented graph, $Y\subset V$ be some fixed set of its vertices. Call $A\subset V$ independent if there exist $|A|$ vertex-disjoint paths starting in $A$ and ending in $Y$. It is not hard to prove this independence system is actually a matroid. Indeed, matroids arising in this way are called gammoids.

Menger's theorem (in Goering's form, I think) states that the rank function of this matroid is given by

$r(A)=$the minimum number vertices which may be deleted so that no path from $A$ to $Y$ remains.

Is there any matroid interpretation, or matroids-assisted proof of this?

I saw some papers in which both Menger's theorem and matroids appear in the title, but on the first glance they deal with usual cycles/cuts graph matroids.