Sorry to hear you lost a chicken.
My opinion would be that the segment you are seeing on the poop you posted is clean and dry looking and therefore more likely deposited on top of the poop after it exited the body rather than have come out with the faeces themselves. I also think that the segmented sections of a tapeworm illustrated in the picture above have been magnified to quite a high level and are not actually visible to the naked eye or certainly not clearly enough to see the segments, so I would be inclined to assume that you are seeing feather sheathing which has landed on the poop after it has evacuated the body or possibly even been blown in the wind and stuck to it.
I'm not sure if it is the same for chickens as it is for horses but a faecal worm egg count will not indicate a tapeworm problem in horses as the segments are relatively few in number and large in themselves so may not show up in the sample taken and looked at under the microscope, but my understanding is that each segment contains thousands of eggs which disperse at a later date into the pasture.
It might be worth considering getting a necropsy done on your chicken to determine the cause of death if you haven't already disposed of her.
After reading and looking at lots of pics, I am thinking that the segmented pieces are dry feather sheath being shed.
I may just do a maintenance de-worm since it's been so warm and wet rather than our typical frozen winters.
Here are a couple of interesting threads about people treating tapeworm in their flock:
Thanks for the links. Very helpful info.
Edited by chxmama - 1/10/16 at 11:38am