I have a Davis Vantage Vue that reads high too when in full sun. Non aspirated, and well over 10 years old, so that may be part of the issue, but has read high for as long as I remember.
But regarding aspiration, not a single temp/rh sensor (66 in total) operated by the NJWxNet is aspirated, but they don't have that problem. Aspiration is good, but not essential; perhaps has more to do with sensor design or just a biased sensor.