Alton Brown recommends mayo on the bottom to create a barrier to keep the bun from getting soggy from burger juices.
But forget about the mayo...regardless of where one stands on proper mayo position there is a much bigger issue with the imperative cheeseburger instructions given: there was no cheese!
I don't disagree, but a lot of burgers end up dry, so the bottom bun stays dry and bland, which makes me sad. Sauce on the bottom solves that, and the top bun gets wet from the tomato. Optimizing for the 80% burger.
The oil in the mayo acts as an aquaphobic barrier between the tomato and the bun. You don't want a "dry" bun but a soggy bun is structurally deficient on top of being bad tasting.
But forget about the mayo...regardless of where one stands on proper mayo position there is a much bigger issue with the imperative cheeseburger instructions given: there was no cheese!