Why do you think that there's necessarily anything wrong? As you make more careful measurements, so it reveals more about the physics of what we call temperature as it relates to different materials.
I can't make out from your post whether your FARS fan was spinning or not, but assuming that it was then the VP2 would certainly have been measuring air temperature, whereas the rain gauge material would probably have cooled below air temperature on what I'm guessing was probably a clear (ie non-cloudy) night, because of loss of heat radiated (ultimately) into space. Put another way, the rain gauge and the surrounding air were not in temperature equilibrium and your VP2 was measuring what it was designed to measure, ie _air_ temperature.
None of this rules out absolutely that there might be a temperature error on the VP2, but radiation cooling of surfaces is a more likely explanation.
BTW, unwetted surfaces in temperature equilibrium cannot experience wind chill.