It depends on the goal you have really. If the goal is to train your dog to trust other dogs then picking her up will be a bad idea (unless there is actual danger of attack). It reinforces the suspicion the dog had that this is dangerous and she needs rescuing. But if the only goal is to avoid an uncomfortable situation, then pick her up. Nothing wrong with that choice, but just know that it will not teach your dog to handle the situation better next time and so the bad reaction will continue.
I have only picked my dog up a handful times. A few times because the dog charging us was actually aggressive (I once ended up at the doctors office with a bitewound and had to get proactive rabies treatment, better me than her I guess) and a few times because the other dog was hurting my dog unintentionally (big clumsy youngsters with poorly developed doggie language jumping on her end running her over).
My dog was terrified of other dogs when I got her. She would scream and pee if we saw a dog across the street. I had to teach her that other dogs were not a threat and I had to keep her at a comfortable distance while we were traning with positive reinforcement and desensitisation. However, sometimes meeting other dogs is unavoidable.
If a dog came up to us and I could not avoid it, I placed myself calmly between the dogs. I let my dog hide behind me without comforting her or making a fuss over it and tried to block the other dog by standing in the way. If the other dog would keep bothering her, I would crouch down and let her hide under me so the other dog could not reach her.
The goal was to show her that there was no need to panic and no need for me to rescue her. She would be perfectly safe on the ground. Sometimes I would pet the other dog and talk to it in a happy voice to show my dog that the situation was not actually dangerous.
I would train from a distance on the lead or have her loose and keep around the outskirts of parks so that she could approach the other dogs at her own pace. Eventually she loved all dogs. She is still not a fan of meeting dogs when on the lead, but she wil greet them calmly if she has to. And if they are rude she will let them know, but she is no longer scared
So long story short if you want the dog to learn how to be calm on the ground, do not pick the dog up as it will slow down any training you do. Give the dog a way to stay safe on the ground, stay calm, remove the dog from the situation if your dog is reactive, but it is better to lead her away than to scoop her up in your arms.
If you are not training and really do not have as a goal to make her calm in these situations (perfectly valid choice as greeting on lead is a bad idea anyway) then ignore what people say and pick up your dog if that works for you
I think especially in the situation described where the other dog is out of control and the owner is not really helping, then why should she have to handle a situation like that? I once let go of my dog (as I knew she would calm down if she had an escape route) and grabbed the strange dog to calm the situation down. These are the exceptions and the normal rules don't apply in my opinion.
