It's not that the response damages their brand. It's that the letter damages their brand, and their response only cues more people into it. It's a lose-lose situation for them once the letter is sent out - unless they had something witty planned and responded with a semi-troll comment such as "like this? present new product"
I believe they did address the parts of that letter that they could reasonably address in public, and they did it in standard corpora-turd-ese which is what their investors and clientele all seem to like. I don't think they absolutely had to respond in the first place, but I just don't see how they're any worse off than they were before.
