Having spent way more time on this problem than I really should have, I'm going to make sure everyone can actually find a solution instead of useless WordPress support threads.
The Problem
I wanted to export all the data from WordPress using its native export mechanism (located at http://YOURBLOG/wp-admin/export.php), but since the blog I was working on was pretty large (6k posts, 120k comments), I kept getting XML files that ended prematurely and for which xmllint spit out this error:
Premature end of data in tag channel
Upon closer inspection, I saw the XML file ended with a random, yet always fully closed, </item> tag, but was missing the closing </channel> and </rss> tags, as well as a whole …