It seems to make sense that Elizabeth is not the boys' biological mother. Since the boys were living with her and Maurice, he obviously knew about them, so there was no reason for her to say on the census that she was the mother of 3 children with 3 living, when if they were her sons, she would have said she was the mother of 6 children.
The boys were living with Lizzie and Maurice in 1895, but not in 1900. Have you found them in the 1900 census? Were they with another family member at that time? Finding them in 1900 may yield a clue.
If only the 1890 censuses weren't lost!!