A little background should help explain President Loeak's apparent endorsement of Amelia Research, Inc.
According to reliable sources, the recovery of the two artifacts at Mili last year was accomplished not by anyone in the American group but by a prominent Marshallese businessman (we know his name) with powerful political connections - hence no need to bother with archaeological permits. According to the article, "(President) Loeak invited the team to visit Mili and has assigned government Historic Preservation Office staff to assist the investigation." The group of Americans sponsored by Parker Aerospace has reportedly now gone to Mili with "more sophisticated equipment to find other parts." RMI Historic Preservation laws require that this kind of work be carried out under the direction of a degreed archaeologist. As far as we know, no one in the group of Americans has any archaeological training. The RMI Historic Preservation Office currently does not have a degreed archaeologist.
We can only conclude that whatever searching is being done at Mili is being done without archaeological protocols. Should they happen upon historically significant artifacts, whether related to Earhart or (more probably) WWII, the damage done will be permanent.