I think I figured out what's happening. The PC is a Lenovo IdeaPad Y570 with RapidDrive technology. Apparently, this combines both HD and SSD to make it appear that it's one drive, using the SSD for operating system files in a way that's transparent to the operating system; it presents a simple C: drive. The D: drive that I thought was the SSD is apparently a recovery partition of about half of the SSD space with software and drivers on it. So, it's not a real hybrid drive, it just tricks the OS.
There may not be a simple way to have a defragmenter work on just the physical HD.