Of course, I totally understand! I have the exact same privacy concerns as you. It is daunting when an app asks for access to something super personal like your contacts or photos.
I can’t speak for Monzo here, but I’d imagine that although that language is vague, and like you say, leaves them room for uploading a partial version, they do say:
I imagine the “full” language is used because when there is a match, your device asks Monzo’s servers for information such a contact name and their Monzo profile picture (so they can display them nicely in the app). So during this process, they will technically discover a link between two users if you both have each other as contacts.
Just a guess from my part. I’ve not had coffee yet so that might seem just like an incoherent ramble, so apologies if it’s the case! 
Also, I just want to point out, in my experience, Monzo isn’t one to lean on using non-explicit language to catch users out, or do things maliciously but creating “outs” by using vague language. They’re really upfront and transparent about their rights, wrongs and everything in-between. It’d really surprise me if they used language to trick people.