Thanks for answering!
The other styles are all "based on" Normal.
I just noticed something in the navigation pane that's a little confusing.
Some of the non-header text has an expansion down arrow in the navigation pane, which means Word recognizes them as "header" styles (they're not), but you can't promote or demote them - those options are grayed out. I was able to confirm that this is the text that's displaying in the TOC inappropriately.
I tried copy/pasting the entire document into a new file, and it retained the attributes in the navigation pane, as above. So it isn't the file.
When I open the TOC dialog, I can see that the wrong styles display as Level 1 (it should only have Heading 1 and Heading 2) but I can't delete them. I would expect to see that option here. The Options and Modify buttons didn't give me the option to select or delete either. Is it somewhere else?