In reply to Malcolm Blaney.

I should have guessed about Twitter-atom, but then when looking at it again I notice that the app itself actually has a radio button toggle for switching between the two! PEBCAK!

I keep a number of OPML files available on my website if you want to run some tests. I was honestly surprised that I could even put in a URL to any of them and have your reader begin to pull any of them in. As a caveat for troubleshooting, I'm using the older OPML v1(?) spec built into WordPress and not the more recent one and that may have caused the issue. There may also be some sites listed in some of the files that don't actually have feeds associated with them and that may be another cause of the problem.