The index.bdm file was probably named that way on the original card, but appeared as INDEX.BDM when mounted on the Mac. FAT32 is not case-sensitive, and OS X's file system code (specifically the NSFileManager class) programmatically presents FAT32 contents in uppercase. OS X can open AVCHD content, even with a filename in lowercase, from case-insensitive media, like FAT32 or HFS+ in its default, case-insensitive mode.
However, when you copied the AVCHD content to a case-sensitive filesystem, the true nature of that lowercase filename becomes visible (it doesn't get renamed as lowercase, it simply gets revealed as lowercase to begin with!). OS X / QuickTime get confused by the lowercase name, and you get the dreaded "CANNOT OPEN".
The fix is to ensure that all the AVCHD-standard files and folders are in uppercase. As you see, the folder tree above the INDEX.BDM files loses its special status, but the INDEX.BDM file can be double-clicked to open the AVCHD browser. Just as importantly, editors like FCP X and FCP 7's Log and Transfer window will properly see the media even on the case-sensitive filesystem.
I encountered the same thing copying AVCHD to a Linux-based NAS with a case-sensitive filesystem. In my case, my Panasonic cameras will write an INDEX.BDM file when I erase all clips or format the card in-camera, but if I erase just one or a few clips, the file gets written as index.bdm. According to the response I got on a bug filing, Apple considers this a bug in Panasonic's implementation, and Apple won't be fixing their code to allow reading AVCHD from folders with mixed-case folder names / filenames. So I'm writing a utility to walk my folder trees and make sure everything is uppercase, grumble grumble...