A1-weak equivalence versus isomorphism for quasi-projective surfaces

Determine whether an open subscheme of a quasi-projective surface that is A1-weakly equivalent to the affine plane minus finitely many points must be isomorphic to that complement.

Background

Theorem 4.5 proves that, when U is an open subscheme of an affine surface, being A1-weakly equivalent to A2 minus finitely many k-points is equivalent to being isomorphic to that complement. The paper explicitly notes that the corresponding statement for quasi-projective surfaces is unresolved.