The plus operator in the page appears to be binary rather than unary. I've never used it. Is that affected as well? (Though I'm confused why AND is necessary. Isn't it implied normally?)
That is correct. AND is added by default and is never necessary in Google.
It's a little confusing because fo how Google implemented some of the operators. The boolean + operator in many cases is used in the same way as AND, but Google originally used it to let users to force a specific word to be present in a search result.
So a search for Fish +Chips was a search for both words, but 'Chips' MUST be present. The equivalent search today is Fish "Chips". It's a little annoying because it requires typing another character, and it it is still not always respected.
I think the default is more like AND/OR. If AND were the default, and I put a list of five words in without any 'AND' or 'OR', then I'd expect to get only pages that have all 5 of those words. Now of course google looks for synonyms, unless you put quotes around each search term (which ostensibly blocks synonyms, although as you and others mention, this doesn't always work). But afaict, returned pages don't even necessarily have synonyms for all five search terms. That's especially true for words that don't have much semantic content, but it seems to be true even for very specific words. And that's more like OR.
