Webview can be done quite well if it is done correctly. Did you know that most everything in individual messages in the Gmail app on Android is done with a webview?

The reason it is fast though, is it is not loading that webview from a website, but building it from data locally. That gives it a native app speed.

On the other hand, the original Google+ release for the iPhone was bad because it was pretty much a webview downloaded on demand too.

Facebook is just loading it on demand basically as a webpage.

So it's possible Twitter is using a webview, but downloading the data separately for speed.