In Washington state in 2002, Lydia Fairchild nearly lost custody of her three children, when a test revealed that none of them shared her DNA. It turned out that Fairchild’s body was populated with cells from a non-identical twin she’d unknowingly had before birth, making her, in effect, the biological aunt of her own children.
The technical term for Fairchild is a ‘human chimera’: a human being composed of cells that are genetically distinct. The phenomenon can happen artificially, through a transfusion or transplant, or naturally, as in Fairchild’s case, through the early absorption of a twin zygote.
I don’t know if this is a widespread practice among twins, but the author refers to non-twins as “singletons”.