In "Family," Picard's brother Robert groused that their father always favored Jean-Luc. In Q's "afterlife," however, Picard's father castigates him as if he's the family screw-up. Picard is deeply unsettled, showing that the apparition's behavior strikes true. Clearly, both Picard boys had the same issue with their ferocious father.
Picard comes across Q in the Enterprise's sickbay. What if Q was there for his usual messing with the Enterprise's captain and just bumped into Picard.