I may have uncovered a WP bug (or oversite).
I guess I made a mistake, and named a parent page by a name, let's say: "plumbing repairs"
while I also named a category by the same name: "plumbing repairs"
I then created a child page, let's say: "leaky faucet"
and finally created a post under the category (plumbing repairs) with the same name: "leaky faucet".
So in the end, I had created two pages with exactly the same URL -- and WP did this for me with no error message or warning.
For several minutes my site was inaccessible.