Phrases like "second DIRTY bit" were simplified, and refered to a second setting near the expected (first) "DIRTY bit". I've now verified it (with anUSB flash drive, and FAT older than FAT32, and OS/2's FAT):
In FAT mode, DFSee's Set FAT status Clean sets both settings right. The expected classic DIRTY bit, and the unexpected second setting. DFSee prints both lines, one per setting.
The component (FAT and/or USB) of OS/2 may be outdated, because OS/2 may have to check or set both settings. Apparently Windows 7 checks both settings, and OS/2 sets one setting. DFSee checks and sets both.
If needed I can attach image files again, if one still wants to research the orginal wrong situation.