The woman definitely initiated the attack on the deer. I don't blame her for defending her dog, but the dog was safe under the car by the time she tried to do a Ruth Buzzi on the poor thing.
I'm not sure where the deer started out, but it was already terrified after it came out from behind that shed and stumbled on the concrete. Just a bad chain of events with bad timing, it seems. I have to think that if it hadn't been for the dog attacking the deer first, and then the lady going after it, it would have just wandered off peacefully. The dog went after the deer while it was already spooked by whatever scared it out from behind the shed or at least scared because it had stumbled on that slippery concrete. So I feel like the deer was just defending itself from what it perceived as an attack.
There have been a number of cases where deer have attacked and gored or stomped people. They're not to be messed with. But generally, deer are either scared of people or very mellow. So I suspect that there are usually some unusual circumstances that lead to people being gored or stomped. But I still wouldn't purposely mess with them.
We get a lot of them at and near my house and in the whole neighborhood. I came home from work one night in the wee hours, and heard a ruckus in the bushes along the front of my house next to the porch as I was getting ready to open the front door. Within a few feet of me, out popped one, then another, then another very large bucks who had apparently been snoozing in those bushes. I hadn't seen them at all until they woke up and decided to book it! They ran off out into the yard and just stared at me, so I went inside. But alas, after I rounded up my camera and came back out, they'd wandered off across the street to the neighbors' place. They could have easily hurt me if they'd had that in mind.
We get a lot of security camera captures of deer. Usually, they're murdering our bushes and trees, but not bothering the people.