If you look at the source the actual text of that paragraph is what gets copied, they just use some sneaky CSS to make it not visible. It's not explicitly marked as hidden.
But there are so many other tricks to hiding text -- margin-left:-10000px, font-size:0, color:white, and so on, that there's really no way to avoid this.
So I can't even imagine how a browser extention would 'fix' this -- no matter how clever it tried to be, there would almost always be some way around it.
The browser can generate some kind of map for which region of the screen is what font. If you don't have to guess the font, OCR should be easy and reliable. That takes care of the hidden text issue. But second, it means one would be able to copy/paste text that is in an image (because some web designers hate you).
You could do a per character visibility test at the time of copying, but sometimes you want to copy test that is not currently visible on your screen.
For example doing Ctrl+A in a document.
http://amiga-fish.erkan.se/amiga-fish-disk-968-content-Power...
You could probably modify your browser to defeat this trick, but doing so you would run the risk of breaking existing sites and making CSS even more complicated than it already is.
And malicious code writers would simply switch up their code to a new trick.
Yes, it's probably not easy to fix, and once fixed there are probably a dozen different ways of cheating. I'm just pointing out that it's certainly possible to fix this particular attack vector.
If you right click and say 'copy link' you'll get the t.co URL, but if you select the partially rendered URL and ^C you get the full (non-shortened) URL in your clipboard.