I looked at this again a few minutes ago, and yeah, it's really odd. When I added a Text layer to illustrate the issue, the error with the persistent round cap end went away. When I removed the Text, the end remained flat, but when I undid it back to before I created the text, the round cap was persistent again (that is, it remains round after disabling Round Caps.)
The side with the flat-end cap flips around with the bezier handle, which it shouldn't do. After I reset the point's curvature, it works correctly.
I didn't do anything special or unusual to create this curve; I just disabled Round Caps.
I saved the bad version of this project and will send it to LM for evaluation. If you have an example file demonstrating the bad stroke, I suggest doing the same.