If you have worked in IT for large corporates at any time in the last decade (especially if you are at the decision making level) you would have been invited to an endless stream of vendor lunches promoting Data Warehousing and CRM products. The only vendors that are able to supply the NSA with infrastructure on the apparent scale they are operating at are the usual suspects in the top tier enterprise market. They are building massive aggregated data repositories that are probably technically 'legal' if you look at it from a certain conceited angle.
Dishfire, PRISM, MUSCULAR, Fairview etc are 'operational systems' that feed raw data into the ETL Layer and are completely insulated from the end analysis of data. Snowden claimed that as a consultant, he could look up data on anybody, so there appears to be a monolithic aggregated data warehouse, or more likely, a federated database system offering a common schema to query constituent databases internationally (I have written more than my fair share of proposals and documentation).
On the output side, Data marts at various levels of classification let them dig through the dataset. XKeyscore is an example of an internationally available tool that queries a data mart that provides a selection of intelligence information to friendly intelligence agencies. It is query based, and will gather information on those queries based on a 24hr - 30 day buffer, but if something of particular interest is discovered, more precise queries can retroactively gather additional information. This is a data mart with a relatively small 'Operational Data Store' attached to a data warehouse system.
If UK had, under the umbrella of UKUSA, access to a data mart that provided them with a subset of the aggregated NSA data that excluded UK citizens (apart from those allowed under Anti-Terrorism acts), that would be kosher, in their humble opinion. Likewise, the US can build data marts that query the warehouse excluding US citizens. The UK can submit information that it has 'discovered' about US citizens without penalty under UKUSA and vice versa.
The US is probably also free to build highly classified datamarts that directly query the entire data warehouse, stricly for use in extraordinary circumstances. You know, in case of war, or martial law or something. Ok, just this once....
It is tempting to see what the US is doing as some sort of Manhattan Project of surveillance, or 'Skynet', but the reality is far more disappointing. The whole thing is standard enterprise architecture practice, and owes more to IBM Rational System Architect than Orwell. If you want a vision of the future, imagine a sales consultant clicking through powerpoint slides - forever.