I added an external documentation site (publicly accessible) to Sharepoint [Search Service Application > new content source, created a crawl rule with that URL, and verified that the site was crawled correctly.
I then created a search results page (called Reference), and filtered the results based on the path.
For some reason, when I search 'Everything', I can't find any results on that external path, but when I search Reference, I see what I'm expecting.
Sharepoint is indexing my site correctly, and is returning the results in some situations, but not others, and I don't know what the difference is.