I wonder if Obi-Wan would have actually strayed that way. Although he is somewhat impulsive in nature in Episode I, he matures greatly by Episode II, when he verbally reprimands Anakin in front of Padmé: “And you will learn your place”, essentially saying some of the same things that Qui-Gon was telling him. Obi-Wan became the quintessential “old school” Jedi Knight — believing in the Jedi Order and loyal to a fault. And especially with the utter betrayal of Anakin, a man he considered his brother, I could see him sticking very closely to the “no attachments” rule.
That said, this is my very favorite theory about Rey. It makes good logical sense, would create a great story that now spans two families… and I so very much want it to be the case.