The person who emailed GRRM is a JB SHIPPER. We don't have a screenshot of exactly what she wrote because there was a lot of personal information. We tried reaching out to get a screenshot of the Jaime and Brienne content, but it seems like she's no longer in fandom. BUT we have a general description of what she told him. She was displeased with the treatment of Jaime and Brienne, so she wrote about her personal struggles and why she related to the characters, particularly Brienne. She mentioned that she wasn't going to accept the show's ending for them, because the messages associated with that endgame were upsetting and nihilistic, and she was looking forward to an ending that was more inspirational and hopeful for that pairing.
That's what we know.
What we THINK is that she mentioned the dream, because he randomly references it in the email, so I believe the first part about "your analysis" is in reference to her dream interpretation. Considering she's a JB shipper, and from what I remember, her dream interpretation and analysis of the characters aligns with the average JB shipper: foreshadowing Jaime and Brienne being a romantic couple, Jaime outliving Cersei, Brienne outliving Jaime, Brienne's light being symbolic of carrying on the Lannister legacy, etc. (I have a slightly different interpretation than she does, but I've seen her mention these points in the recent past).
GRRM: "Let me say this much –– your analysis is close to the truth. The butterfly effect was at work since the earlier seasons… and it changed some storylines more than others. If truth be told, I'm to be blamed for this too, because I had a load of work and I had to gradually step down from my duties after the forth season to concentrate on Winds. I haven't read the scripts of the last two seasons. And I wasn't exactly a fan of sacrificing some characters and stories at the expense of others… but I do need to mention that it was also an issue beyond the writing room and creative process.
The priority of a television network giant is rarely the story and the messages it gives. The desire of David and Dan (and HBO) to focus on actors like Peter and Lena is understandable. Sometimes certain scenes are written only for actors or for their memorability. And it's not a bad idea to end a TV show which is well known for a controversial incest scene, with another memorable scene of the incestuous twins… it's an ending. It makes sense in this medium, because it's a medium that mainly relies on the memorability of imagery. A finale which brings two or three main actors together is more powerful. It's a different animal when you are only dealing with characters, and not actors. The power of the ending in a book relies on the emotions which the words and the story itself convey.
I feel for you and understand your concerns, but I think you will be more satisfied with the books' ending. Imagine that the books are the show are two parallel universes. There are two Briennes, two Jaimes, two Cerseis. Have you watched Sliding Doors? Sometimes taking a different path changes everything. Have you noticed that the dream might have more than one potential ending? Is Jaime's ending in the show necessarily "wrong"? Can't it be an ending which was the result of choices made and paths taken (by more than one character)? What if Jaime caught the train in one universe and missed in the other? Just food for thought…"
tldr;
1) GRRM talked to a Jaime x Brienne shipper who related Brienne to herself.
2) GRRM strongly implied that Jaime and Cersei don't die together in his ending.
3) Jaime and Brienne's ending will be a bit more hopeful/less nihilistic and believes the fan will like his ending more.
4) He didn't read the scripts for the last 2 seasons.
5) The show is considered a parallel universe for him where characters make some different choices.
6) He mentions that he's unhappy that the show sacrificed some stories and characters for the sake of others.
7) GRRM says that finales between books and shows are different because one deals with characters and the other with actors. Different mediums allow for different things.