I'd have gotten the doll if I was just sitting outside, waiting for her to stop crying. And, honestly, my 11 year old might cry for her toy or her book or whatever, this sort of thing comes up all the time in my family. My main reason for not going to get the doll would be because I didn't want to get up and leave the table and go out to the car, but if I had to get up and go outside the restaurant anyway, I'd figure I might as well just get the doll.
But if I was inside and I didn't want to get up and leave my dinner in order to go get her doll, I wouldn't have, I would have found something else for her to do, or I'd have interacted with her more. It's not so much about making sure she follows through with her choice, for me it's more about the fact that if I've given a warning like, "if you want to leave your doll in the car, that's fine, but I'm not going to want to get up and leave my dinner to go and get it if you change your mind" then I probably have a reason that was important to me. I find my children are often not really respectful of that, they just really don't care how I feel and part of growing up is learning how to respect that their parents have needs also, and are not always willing to cater to every request.
My child wants me to go against my own desires because her need is important to her, and usually my children will escalate it until the negative aspect of doing something I didn't want to do is outweighed against the negative aspect of dealing with my child's behavior because she wants what she wants. So then it's a balancing act between my child's need and my own need. At that point I have to ask what my goal is and what is the best thing to do for both of us. If I feel like my child is complaining because she is truly sad and upset, I can talk to her about that and then agree to do what she wants or come up with a mutually beneficial compromise. But sometimes I feel like it's angry behavior because they know that acting out will change the dynamic in a way that is favorable to her, even if it's not to me.
I can see why the mother would do what she did and I think it could be a good thing. Maybe she wanted to go out with her friend and the child insisted on coming along, that she wouldn't be bored, so the mother decided to see how she would do and let her experience it for herself. Or maybe she really wanted her child to get to the point of realizing she wasn't going to get the doll and figure out another way to entertain herself, which would probably come after accepting the inevitability of the situation.
Personally, if I got into the restaurant and realized that leaving the doll in the car was a bad idea, and I thought that getting the doll would let me have some free time to talk to my friend, then I'd have gone right back out and gotten the doll. Or more likely, I'd have found a pen and paper in my purse and let her draw. Or I'd have handed her my iPhone and told her to play a game. I'm often not good at letting my children figure it out for themselves, I just want them to be quiet.