I can confirm the experience that sometimes searches for quoted terms yield pages that do not contain the quoted term exactly. I don't have a specific example from the top of my head.

Is it possible that the results simply don't exist and instead of giving you nothing it gives the next possible match?

It could be this - but you would notice it after opening the search result.

I spend some time reading a random website until I realize the sentences i was looking for is not there. Useless and frustrating.

I just tried https://www.google.com/search?q=%22I+used+this+quite+frequen... and it works for me now, but I definitely recall having problems searching verbatim before, perhaps they improved/changed it recently?

works for me too, maybe being in europe does the trick?