Bérczi et al.'s reduction conjecture for coverable matroids

Let $M$ be a matroid whose ground set can be covered by $k$ independent sets; such a matroid is $k$-coverable. A reduction of a matroid is the reduction notion used in the source, and a partition matroid is a matroid whose ground set is partitioned into parts with independent sets meeting each part within its prescribed capacity. Bérczi et al.'s conjecture. Every $k$-coverable matroid can be reduced to a $2\cdot k$-coverable partition matroid. The conjecture asks whether reductions to partition matroids can always increase the covering number by at most a factor of two; the provided source does not state whether it has been resolved.