Responding to Dennis Patterson's post today, ArcMap does not apply any Geographic (datum) transformations automatically. When the warning appears about the Geographic Coordinate System differing from other data in the map, a Geographic (datum) transformation must be selected by the user. The best resource for selecting the "best" transformation method is the list linked to Knowledge Base article 21327. This provides the names of available transformations in alphabetical order, the WKID, the accuracy of the transformation in meters, a verbal description of the area of use, coordinates for the extent for which the transformation should be used, and the transformation method and parameters.
21327 - Select the correct geographic (datum) transformation when projecting between datums
From the description in the case above, it sounds like the imagery did not have its' projection correctly defined. Could have been in decimal degrees in a Geographic Coordinate System, but defined as a Projected Coordinate System by mistake.