I think I've come across a good answer. While I don't seen anything like this in the LOTR trilogy, it is an idea present in Tolkien's work. I was reading The Hobbit when a quote struck me. Having escaped the goblins of the Misty Mountains, the party meets up with Beorn. After breakfast they discuss their route to Mirkwood. Beorn says the following:
"Still you are safer going north, even though you seem to be going back nearer to their strongholds; for that is what they will least expect, and they will have the longer ride to catch you."
To me, with the wording so similar this is pretty clearly Jackson's source material for Pippin's stroke of genius. I may be wrong, but it feels like the right fit. Given Bilbo's love of telling stories to the younger Hobbits, he may have even passed this along to Pippin, planting the seed.