Budur's weak conjecture on Bernstein–Sato zero loci

Let $B_F$ be the Bernstein–Sato ideal associated with the tuple $F$, and let $Z(B_F)\subseteq\mathbb C^r$ denote its zero locus. Budur's weak conjecture. Each irreducible component of $Z(B_F)$ is a translated linear subspace of $\mathbb C^r$ defined over $\mathbb Q$. This is presented as a weak version of Budur's conjecture on the structure of generators of the Bernstein–Sato ideal; the supplied text gives no resolution, so the claim remains open.