The time and location is said to be based on a number of detections and non-detections of several "sensors", without clear indication whether these are groundbased or space based sensors (see my previous post here) but I do suspect the latter are involved. The more so since the only ground-based tracking stations in this wide area are on Oahu (Hawaii), Kwajalein and Guam, and none of these would be able to pinpoint this location so exactly as this location is out of their detection range [edit 28 Sep: plus, the final UARS track did not bring it in reach of Guam and Kwajalein anyway]. The description by NASA's Johnson in the video appears deliberately vague to me. [edit 28 Sep: there is of course always the possibility that they happened to have a tracking ship in the vicinity].
I have some lingering concern in the back of my mind about the "neatness" of a reentry at exactly 4:00 UTC (nice and round), but sometimes such coincidences do happen.
Below is a map of the now released reentry point.