Okay, but they’re not “hosting” anything (other than the script). They could take down the server with that script on it and the markup would show up fine. If Twitter went out of business tomorrow, all these tweets would magically show up again. But no, they’re going out of their way to break your webpage. That is absurd.
You are using content from twitter on your page and then using a script from twitter to format the content, right? You've seeded control on how it's displayed. They changed their mind on how to format the content. You are responsible for your page no one else.
This is kinda like asking someone who just got robbed “Why did you leave your door open? You’re responsible for your home no one else.” That’s true, but it’s still not okay to rob people!