Even the college didn't take the claim seriously; it isn't mentioned in a college publication until 1874, and itsn't called the Wren Building until the mid 1920s.
My personal guess:
It is possible Jones is purposely lying, but I'm willing to give him the benefit of the doubt. He may have misunderstood:
William & Mary was granted a seal by the College of Arms in 1694. It depicts a campus based on Oxford. Central to the seal is a building that looks like the Sheldonian in Oxford, which Wren Did design.
I suspect Jones, who joined the faculty in 1717, heard from an older colleague that the seal was modeled on Wren-designed buildings.
It seems impossible that the struggled college & colony wouldn't have immediately cashed in that Wren connection
Why does any of this matter, or relate to this class?