It's weird, but he doesn't really have anything to gain by doing the medical testing. It's not that much different than when players only do their drills at their pro day.
He has some ego, but I don't see much that I think will hold him back from being an upper-eschelon starting QB. Well except maybe being drafted by the Bears.
EDIT: I was going to mock the Bears for being around since 1920, yet Mitchell Trubisky, as awful as he is, ranks fifth in their history in passing yards, but then I saw that Rick Mirer is fifth in our franchise history, so I decided to stop examining further.