Is this just a non-technical person attempting to inject a little detail into the article? My first thought was, "How would I do this in JS?" and it took me a second to decipher that sentence.
I am not HTTP expert, but my understanding is that a 301 is a RESPONSE not a REQUEST.
What is most certainly happening is that Twitter is making a HEAD request to URLs to see if a redirect is happening. The http redirect is a RESPONSE of type 301 (permanent) or 302 (temporary).
And yes, I suspect this is happening somewhere that can be cached. It would be easy to tell by setting up a 301 redirect, posting it to twitter, and watching the server logs.
the phrasing of that is a bit weird, but they probably test until they no longer get a 301 or 302 redirect and save the result. they print this result on the front end as a title for the link and as an HTML5 data attribute "expanded-url" on the link.
1) XHR cross domain policy prohibits requests to domains other than the domain the page loaded from
2) the XHR GET method always follows a 301 redirect and returns the content at the URL. The full URL is not made available.