If I set a category to products only, it shows products only.
if I set it to static block and products, it shows the static block and products.
If I set it to static block only, it shows static block and products.
That last one doesn't seem right to me. Any idea how I can get it to show only the static block? Or why it insists on showing the products as well, when the backend drop down is on static block only?
The answer is: Reindex EVERYTHING.
I had foolishly assumed that the category data would be covered by the index called "Category Flat Data". However, it was not until I reindexed "Product Flat Data" that the category showed correctly.
I don't like to answer my own question, so if anyone can tell me WHY I needed to reindex product data to get the category to display correctly, you get the shiny green checkmark...