Interesting discussion. Nobody knows what animals think or why they do what they do.
Those who study the brains of us and critters suggest that they lack reasoning, which is of higher intellect, but they do have "memory" so that once they've had a bad experience in a given situation, they "learn" from it instinctively, sorta like we (some) shoot instinctively and hit the mark.
Process input? Surely one would have to say so to have memory reserves...reason out a logic that to let this or that go ahead or to look up once having seen something frightening in trees?
That one seems more like a stretch to me...
There were words I learned called "Operent (sp?) Conditioning" meaning that that experience creates positive-negative memory and intuition keeps animals from repeating threat situations.
I've seen what Sam said, specific to a particular TREE even where some guys hunted regularly... Big doe even side-stepped (never saw that before) 4-5 steps to get a better angle and then resolving (?) there was no figure in that tree, went over to lie down with the fawn.
Given the "maternal instinct" of does, I wonder if she may have drawn the OP's attention to let her offspring saunter away who mimiced Moma's blowing and snorting?
Fun to speculate though, isn't it?