Imaginary Friends

I have read that it is rare for twins to have imaginary friends, presumably because they have each other. What would the psychology textbooks have to say about my twins sharing an imaginary friend, and that imaginary friend being their father's real-life sports hero? Disturbing on so many levels.

This morning, at the coffeeshop.
Me: What are you doing upstairs guys?
Jacob: Tom Braden is up here
Me: Excuse me?
Molly: We're talking to Tom Braden
Me: Okay, can you see if he wants to join us here at the table for some muffin
They return to the table
Me: Do you guys want some more muffin?
Jacob: Tom Braden does (takes muffin and shoves it into his closed fist)
Me: What are you doing?
Jacob: Tom Braden in there (pointing into his fist)
Molly: I have Tom Braden in my hand too
Me: Really?
Molly: Yes, two Tom Bradens

At dinner tonight, Jacob subjected me to an inquisition and looked really incredulous when I had to admit to him that I'm not friends with Tom, that I've never met him, don't know where he lives, don't know what he's doing tomorrow, etc..

So, Jacob might be the only person jumping on the Tom Brady bandwagon at this juncture of his career. Part of me also suspects that Jacob might just be yanking my chain, intentionally mispronouncing Brady's name, taunting me by pretending to be friends with my idol. I wouldn't put it past him.