There are two text frames; an upper one, across the top, that is supposed to have the header only, and a much larger one below it, for body text.
The problem is that the header text is doubled so it appears below the header, and oversets, and does not have to be in the header text frame. Or in any text frame, for that matter, it just oversets whatever is there. I can change the leading between the "real" header text and it's shadow text, moving it up and down to my heart's content relative to the upper, real text, but I can't get rid of the shadow text entirely. If I expand the upper text frame, the one for the header, the shadow text is still there but I cannot manipulate or delete it, it's not part of that text frame. It appears to overwrite everything. Likewise, shrinking the upper text frame doesn't make it go away, nor does moving the lower text frame. In fact, on a page with only the header text frame, I still have the shadow text, outside of the text frame.
The header is invoked as a section title; if I just enter it manually, I don't get the shadow. That is, just typing something in to the header is not a problem. It's only when I use <section title> in the master page header that I have a problem, so pretty clearly that's the root of it. Now why, and what to do with it, is another question.