I agree with your observations. Google search seems to completely ignore search terms in quotation marks. It's like the search favours showing somewhat relevant results instead of nothing at all.
Google search is however personalized per user account in mysterious ways, so there's that at play as well
In general when I've landed on apparently unrelated pages and checked this it's been true.
This is often an anti-feature though - if I search for an exact match I probably don't want pages that don't visibly include it.
I am strongly reminded of the days when AltaVista searches had started turning up more and more spammy garbage and this young upstart with a funky name turned up to challenge them.
I reckon Google's crown could be grabbed by the end of the decade. Sooner if they're slow reacting to a challenger.