Obviously, there's something off about Picard's original genetic structure, something he's passed on to Jack. Vadic suggested that Picard's diagnosis of Irumodic Syndrome was actually something else... so, what might that be?
I doubt the writers would shoehorn in some random incident from before TNG or after Nemesis that the audience has no knowledge of. What does that leave? I don't recall Picard ever having his genome fiddled with by anyone, unless it's going to be something silly like prolonged exposure to someone from the Q-continuum warping human genetic material.
What could Picard have passed on to Jack that makes him telepathic?