Promethium has no stable isotopes; the longest half-life is 17 years. There is none to be found anywhere in nature. Therefore mining for it is not possible.
At the US Naval hospital, American flags are shown hanging vertically with the blue field of stars on the upper right-hand side. Flag protocol states the field should always be in the upper left, whether displayed horizontally or vertically. An American military site would know this.
In a military hospital in Guam, a dummy, the kind of which Annie placed in the bed to distract the attackers, is unlikely to be found.