I don't doubt it after seeing videos of man vs deer .Especially the "tame " deer that people keep !
Deer also know their territory very well . They know for example that a storm will knock down apples and they know exactly where all the apple trees are. I've watched them come onto my property after a storm , go right to an apple tree , take the apples knocked down , then leave ! I've been told by hunters that the deer they were going to shoot "just disappeared" !!
I walked down a trail and came across a fallen tree. I stepped over it [I'm 6'1"] then noticed a deer track went UNDER the same tree ! Yes about crawling on hands and knees. Or a deer that jumped through a barbed wire fence that had strands 12" apart !