This is not a bizarre phenomena.
Have a look.
The human tear ducts secrete what is in essence simple silica, though I for one cannot explain why.
Silica is a base component of sand, rock, and yes, diamond.
When you get up in the morning and have "sleep" in your eyes, its, well, crusty, ain't it?
The "crusty" part is the silica base extruded by the tear ducts.
I looked into this story a long time ago when it happened (and it was a long time ago).
They may not be real diamonds, but at the most - simple glass.
As you know - glass is also a silica base.