I see why you are holding fast to this point. I just did a search on Google using "Burke" and "Mary Therese Helmueller," and lo and behold, the first hit I get is a story from the National Catholic Reporter, which many know is your favorite publication.
It's this story, linked in the NCR.
Since you can't prove the transgendered nun story wrong, I tend to believe it, given the connections. That would tend to make most of the rest of it true, as well, unless you can disprove any of it.