Hi Ray,
Import Wizard is an administrative migration tool.
The reason it works best with Administrator is that it needs to have access to all the objects being migrated - that includes their dependents, parent objects, etc.
The Administrator account has the necessary rights to make sure any infostore query that runs in the background when IW is gathering information parses without any access issues / restrictions.
As Jawahar has pointed out, you could create a user to be used for IW and add this to the Administrator's group. This provides this user the same access as the Admin - but "isn't the actual Admin"!!!!
-Sid