You've made some good points there but I think she yells, grunts and flails in public because she doesn't like the environment (e.g. loud noises, bright lights, too many people). I would also suggests he brings noise cancelling headphones, her phone/iPad with Spotify downloaded so she can listen to music to help block the noise out, stim toys and sunglasses so that she copes fine with being in a public place.
As an autistic person myself, when I go out to public places, I always bring stim toys and ear defenders with me to help me block out loud noises and cope with anxiety/stress.
In addition, he should immediately stop filming when she yells/has meltdowns/shows signs of being overwhelmed, take her somewhere quiet and give her a stim toy and that will allow her some privacy. Nobody wants to see an autistic child or adult melting down in a place for the whole world to see.
And another thing that frustrates me is, why isn't he teaching her to express how she feels and sign that she wants to be left alone. That will enable her to have her needs met more as I think she mostly gets frustrated due to unmet needs.