The slide I'm talking about ( http://www.washingtonpost.com/wp-srv/special/politics/prism-... ) states: "collection directly from the servers of these U.S. Service Providers."

Since there's currently no way to "browse" private data on, say, my Google search history or my GMail inbox, the conclusion seems to be that they either have broad backdoor access, or a specific way of directly downloading from these companies.

In a traditional warrant situation, the data would be collected by the companies and sent to the requesting agency that provided a warrant. Police officers that request, say, HTTP access logs do not download those logs directly.