Well not sure where you are getting your information from ... but it is wrong.
Basename does not only work with files:
$ basename $x
Assuming assetDir is being set further up in your code and your unusual file names are of the format 'SA4TeamSD010::10.91.0.210::Ready::2013151', I would probably use something like:
for file in $assetDir/$assetType/$whichDir/*