Just in case you can't access QGIS
https://dl.dropboxusercontent.com/u/71658964/miconesia.zip
projection is EPSG:4326
I used ogrinfo on the original file and it tells me the projection is EPSG:4326, I think, for example:
ogrinfo -so FSM_adm_SBOC_PCRAFI.gdb state
Had to open data source read-only.
INFO: Open of `FSM_adm_SBOC_PCRAFI.gdb'
using driver `OpenFileGDB' successful.
Layer name: State
Geometry: Multi Polygon
Feature Count: 4
Extent: (137.491872, 1.022685) - (163.051392, 10.036174)
Layer SRS WKT:
GEOGCS["GCS_WGS_1984",
DATUM["WGS_1984",
SPHEROID["WGS_84",6378137.0,298.257223563]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0.0174532925199433]]
FID Column = OBJECTID
Geometry Column = Shape
SID: Real (0.0)
State: String (0.0)
Census_00: Real (0.0)
Proj_10: Real (0.0)
Shape_Length: Real (0.0)
Shape_Area: Real (0.0)
Is it possible that your backdrop isn't correctly projected?
On the other hand I did try to load another layer (a WMS service that includes the area) and there is also a mismatch, the problem is I don't know which one is incorrect.
See WMS service GSJ CCOP Combined Bedrock and Superficial Geology and Age