The interpretation of high proper motion white dwarfs detected by Oppenheim
er et al. (2001) was the start of a lively controversy. While the discovere
rs identify a large fraction of their findings as dark halo members, others
interpret the same sample as essentially made of disc and/or thick disc st
ars. We use the comprehensive description of Galactic stellar populations p
rovided by the "Besancon" model to produce a realistic simulation of Oppenh
eimer et al. data, including all observational selections and calibration b
iases. The conclusion is unambiguous: Thick disc white dwarfs resulting fro
m ordinary hypotheses on the local density and kinematics are sufficient to
explain the observed objects, there is no need for halo white dwarfs. This
conclusion is robust to reasonable changes in model ingredients. The main
cause of the misinterpretation seems to be that the velocity distribution o
f a proper motion selected star sample is severely biased in favour of high
velocities. This has been neglected in previous analyses. Obviously this d
oes not prove that no such objects like halo white dwarfs can exist, but Op
penheimer et al. observations drive their possible contribution in the dark
matter halo down to an extremely low fraction.