Wow.
From their terms of use: "Disney DTC LLC and/or its affiliates and subsidiaries (collectively, “Disney” “we” or “us”) are pleased to provide to you certain websites, software, applications, content, products, and services (“Disney Products” and “Products”), which may be branded Disney, ABC, ESPN, Marvel, Pixar, Lucasfilm, FX, Fox Searchlight, 20th Century Fox, National Geographic, or another brand owned or licensed by Disney."
What Disney is arguing is that their Twitter account is magically a "Disney Service", and that by tweeting at them, and using a specific hashtag, you are magically using their service, which would then bind you to their terms of service.
Fuck right off. That's not how this works.
I understand what Disney wants, it wants to use other people's tweets in their own promotion materials. That is fine, provided they ask permission from the authors of said tweets. But since they're lazy fucks, they're trying to pre-emptively argue that if you use that hashtag, they already asked, and you already said ok, so they don't have to go through the hard, hard, work of actually asking people and documenting their consent.