Just to muddy the water a bit, here's a story that shook me when it happened, but then has just made me smile ever since.
Dad died in 1996, and had a direct cremation. The ashes sat in a box in my closet for about a year and a half until I was able to take them on their final journey to scatter them in his favorite fishing spot in Jamaica Bay (New York City).
All went well, but as I was pouring the ashes into the water, I noticed a small metal disk, about the size of a quarter. I picked it out and put it in my pocket. There was just a serial number impressed in it, obviously how they keep track of the bodies in the crematorium.
After I got back home, I put the disk in the envelope with the cremation certificate that came with the ashes. Much to my surprise, the number on the certificate was one higher than the number on the disk.
So I took care of someone's ashes, but I certainly don't know whose. And someone else took care of my father's ashes. My first thought was to contact the crematorium for the information, but it had been almost two years earlier and I just decided to forget it.
All is well, and at the end of the day it really made no difference.