>don't most programs register a shortcut key or two?
Yes which is exactly why I think it's likely he's being disingenuous about the root cause of this. Shortcut keys typically need modifier keys and, even in the instance where they don't, there has to be some check from the app to determine whether an input field or the main window has focus.
To be clear, I'm not saying it's 100% certain that this isn't an Apple issue but, based on Twitter's track record with their apps, this likely is on Twitter.