This is actually how my brain processes music. Give me a melody, and I will have something arranged on the harp in short order. Probably just boringly obvious chords, but you know, that's been good enough for government work. It's not like I'm trying to sell my arrangements or wow my family with my shockingly novel settings of Christmas carols. Same ol', same ol', usually does just fine for 85% of what I do.
I always figured fake books were some kind of magic tablature, or were guitar-specific, or something. It seems too obvious that they're melody + chords + lyrics.