Ok, there is actually 1 file reported by DIR, and the two directories contain 5 subdirectories. 21 directories if you count . and .. as DIR does. ATTRIB /s /d reports 12 entries, including the recycle bin and system volume information.
Still, 12 is not 11237. And defrag (windows 7) reported that this external usb disk was 75% fragmented. Defrag took around an hour, but after defrag the disk is 0% fragmented, and fragmentation analysis now takes seconds instead of minutes.
The recycle bin is empty (and I've deleted it to get rid of the user entries).
Question: what was fragmented? Why does chkdsk report 11237 files?