It's not the filename -- it's the FID. If you select something from the search menus, you'll get the results in FID order. Now, if you've got your filenames sorted on the PC, then the files will be imported in order, and will have FIDs assigned in ascending order. Thus, FIDs are assigned in the same order as the filenames.

This leads to this small confusion. The player doesn't store the filenames. Ever.