This isn't nearly as spooky as it seems. These researchers can't take a person off the street and say much of anything about what she's thinking. What they are doing is watching the patterns of activity that they observe again and again in particular subjects -- then all they do is match the patterns they see in memory recall to what they've observed over many training trials. It's just a matter of recognizing something that looks very much like what you've seen before many times. 

Furthermore, the part of the brain they are working with, the hippocampus, is active primarily during the formation of memories. Once memories are firmly established in "permanent storage", the hippocampus ceases to react much during recall; instead it looks like the neighboring entorhinal cortex might be a sort of "traffic cop" that directs memory "requests" to the proper storage areas.