I don't think that came from the toilet.
It looks like hard grease cakes that may have come off of the pipes and floated up. Will it float if you put it in a bucket of water?
I've seen stuff like this get knocked off the inside of a sewer line while cleaning it. It is hard and brittle.
Have you had your sewer cleaned recently?
Also you can get a build up in the toilet if you urinate in it and leave it sit. the mineral collect up in the wier of the toilet
Can't imagine this happening. Never heard of such. However, Kohler must have had problems in the past since they gave you a new toilet and did not even want to see the old one. Congrats for taking this beyond the First Line of Defense and getting to someone who could help you!