No, it does not. If it did, Snowden's documents would have contained evidence showing that the NSA either has a copy of the GCHQ wiretap data or that the NSA has direct query access to it, either of which would have been a blockbuster story. There was no such evidence.
Instead, what your quote means is that the parties to the agreement can ask the other parties for any information about their collection they like, and the default response (if there are no overriding rules) will be to return that information. The US cannot ask another country for data about its own citizens without a warrant because, as I've stated multiple times, that is illegal.
You are creating some all-seeing bogeyman by misreading some words. This is better than dredmorbius's comments in that you misread some words instead of not reading them and pretending they said something, but do you understand that misreading words is how conspiracy theories are created?
From the quote of the third link:
> The Five Eyes countries agree to exchange by default all signals intelligence they gather, as well as methods and techniques related to signals intelligence operations.
This seems like a pretty clear implication that a Five Eyes country gets information about its own citizens via automatic sharing of information gathered by the other countries. Whether they technically "asked" for the information or not is not relevant.