Non-Trivial Vector Bundles on Contractible Smooth Schemes

Let k be a field. According to a paper of Asok & Doran, there exist smooth, finite-type k schemes which are contractible in the sense of A^1-homotopy theory (which is stronger than contractibility of C-points when k = C) but which nevertheless admit non-trivial vector bundles. I shall try to explain why this is a terrible state of affairs, and then construct an example.