If you right-click the "Image" in the TOC and select Zoom to Source Resolution, do you see it then?
Often, the checkerboard means there isn't a complete set of overviews made for the mosaic. If you can zoom to the source resolutions and see them (this is making it pull the original .tifs from the source), you will know that the user(s) have permission to see them, and most likely due to missing/incomplete overviews. Though, is a little weird that it is only some users having issues if this is the case.
R_