Bear Down Sunday #4 (and Holding)

With the Chicago Bears enjoying the bye week, it isn't really a 'Bear Down' kind of day. With that in mind, I present a player who wasn't really a member of the Bears or was he?
Jon Najarian is a securities and futures whiz. He co-founded TradeMonster.com and has appeared on many media outlets in Chicago and nationally.
I met Najarian when he worked for WSCR (the Score) in Chicago and appeared at a fundraising bowling event. I didn't get to bowl with Dr. Jon, but I did talk to him for a few minutes.
He said he played for the Bears. His bio states that he was with the Bears from July through October of 1981. Yet, I can find no record of him being on the team. My best guess is he was on the 'Injured Reserve' list for that time period.
If he really played, Pro Football Reference.com would show it. It shows Peter Najarian, who played parts of 3 seasons in the NFL, and is Jon's brother, an options trader and tv personality.
This leaves me to wonder, what is the story of Jon Najarian. Was he with the Bears or not? Believe me, I won't stop until I get to the bottom of this (or at least find anything better to do).

Jon Najarian in Arlington Heights, IL-late 1990's.