  Recently McBreen and Webster constructed a tilting bundle on a smooth
hypertoric variety (using reduction to finite characteristic) and showed that
its endomorphism ring is Koszul.
  In this short note we present alternative proofs for these results. We simply
observe that the tilting bundle constructed by Halpern-Leistner and Sam on a
generic open GIT substack of the ambient linear space restricts to a tilting
bundle on the hypertoric variety. The fact that the hypertoric variety is
defined by a quadratic regular sequence then also yields an easy proof of
Koszulity.
