When jews make a decision for jewy reasons they always cook up and signal boost a cover story. In the battle for late night the kike narrative was:
Letterman was a nerdy socially awkward guy off the air, did not know how to ask for the job. Leno both wanted the job and had a hard charging agent willing to fight to get it for him.
Now the fact that Leno soon fired that agent after she allegedly got him the Tonight Show gig for being a mental case and that she had absolutely no other achievments of similar scale to her name was simply brushed aside. Hollywood agents just go insane sometimes. You know how it is.
When the real reason is: The jews like and trust Leno more than they do Letterman. Not something they can talk about in public. Oh, and NBC was the oldest most hardcore jew network, the flagship. CBS, which sniped Letterman away, was probably out of the loop, or did not care because their late night programming was garbage and Letterman would be an improvement even if he lacked the full shabbos goy merit badge set.