I am using Windows 7 (64bit) and am experiencing the same problem. I do not have "ArcGISFileHandler.exe" on my computer (per Windows 7 search). So what now?
For those of you running Windows 7: if you have redirected your My Documents folder to a network drive you will not be able to use the basemaps or ArcGIS Online. Windows 7 does not allow you to index a mapped drive and the map packages do use indexing. The only way we have found to get around this is to have your My Documents folder pointing your local hard drive.
You are right - I found the file.
So, in that I am experiencing this problem - to where do I want to redirect the unpacking?
It's was set on "Automatically select location". I set it to "D:/ESRI_unpacking". That did not correct the problem.
FYI - I noticed a difference between the versions of Arcmap in my situation. I created the layer package on a computer running ArcMap Build 2800. the users having difficulty reading this file were running Arcmap Build 2414. I recreated the layer package using build 2414 and there were no problems for any user.
Aimee