I wonder if the suggestion is that the disapproval/disappointment that Denethor had as Faramir's father had the effect of Faramir looking to Gandalf for that fatherly approval? And, when he learned it was with Gandalf's approval that the hobbits should go to Mordor with the ring, he made the choice to let them? Hmmm?
That's a bit of chicken-or-the-egg there.
Tolkien never really explains the full dynamics of the relationship between Denethor and his sons. I always had the impression that Denethor's dissatisfaction with Faramir probably predated his relationship with Gandalf. But that the latter helped fuel the animosity between them. Especially since the question of Gandalf was the chief source of disagreement between Denethor and Aragorn in his Thorongil disguise during the finals years of Ecthelion's reign.
What is interesting is the different take that Jackson (and his writers) have on these relationships. Jackson implies that Denethor likes Boromir better because they are so much alike. Tolkien says otherwise: Denethor "loved [Boromir] greatly: too much perhaps; and the more so because they were unlike."
But that is perhaps of a piece with other small character mutations undertaken by Jackson/Wash/Boyyens. Isildur is a conflicted man who comes to regret his decision not to destroy the Ring but is transformed in the film into a largely unsavory character consumed by it; King Theoden is eager to confront Saruman's army head-on but is persuaded by Gandalf to hole up in Helm's Deep where he at least stands a chance against the massive juggernaut - but in the film these outlooks are switched exactly, and not entirely convincingly; Aragorn as a man who clearly wishes to restore the monarchy of his House but doubts whether it can be achieved - but transformed by Jackson into a man hiding from his destiny, unsure he wants the prize at all, even afraid of it at times.
I doubt Tolkien would be entirely happy with all these changes. Though I have to say they are, I suppose, relatively small changes as screen adaptations of great works go. I've seen some that share almost nothing with their books save the title.
If you read Tolkien's letter shredding a horrid script that had been sent to him for review, you realize that it could have been, after all, far, far worse.