Big Willie Weird.
The Twitter embed works by chucking an <iframe> tag in the page (which effectively sets up a whole new web page inside it). Some browsers and even more likely, corporate or otherwise managed environments may block this as there's various ways it can be a security risk.
Twitter may also be blocked or fucked with for some reason.
What browser you on? See if you can open up its "Developer Tools" by right-clicking where the tweet should be, and have a look if there's actually an <iframe> there. Based on what you're describing, there won't be.
