Old timey Baptists use "edifying" as an adjective to mean inspiring or soul strengthening, as in "Pastor, your sermon sure was edifying this morning." The word may be used among LDS folks in a unique way too.
That very well may be the case with the LDS, which is perfect since in your example sentence edify was used correctly. A sermon can educate, illuminate, or impress upon someone a religious/moral belief. Jodi keeps talking about edifying Travis, but in the context of being outside his presence and speaking of him in a positive light to someone else. She clearly isn't using edify correctly