Lee has every right to feel a bit hard done by.
Following his top-10 finish at the Web.Com Tour Championship at the weekend Lee (297th) is now 21 places ahead of Wilkinson on the Official World Golf Rankings.
"It is just bad luck timing-wise for Danny," Duncan Simpson, New Zealand Professional Golfers' Association chief executive said.
"He is clear now but at the time Tim just pipped him. It was a close battle but we were confident that either would be a great representative for New Zealand at this event and Tim has his chance."
The 57th staging of the historic event will comprise 60 players who will play four rounds of stroke play for US$7 million ($8.49 million).