Cornuéjols–Guenin–Margot blocking-number conjecture for ideal minimally non-packing clutters

Let ${\mathscr C}$ be an ideal minimally non-packing clutter, meaning an ideal clutter that does not have the packing property but whose proper minors have the packing property. Its blocking number is the minimum cardinality of a transversal. Cornuéjols, Guenin and Margot's conjecture. The blocking number of every ideal minimally non-packing clutter is $2$. Existing examples described in the source all have blocking number $2$, and the conjecture asserts that this holds for every ideal minimally non-packing clutter; no resolution is given in the supplied text.