It is always more difficult when things do not make sense.
My great-grandmother-in-law had four children born in Chicago early in the twentieth century. The oldest two have delayed birth certificates which incorrectly state they were twins (filed on different days no less), the third has no birth certificate, and the youngest has a relatively correct certificate filed at the time of his birth in 1914 in Chicago.
We've posted the images to our site
http://www.rootdig.com/apgar/
along with an article discussing the records:
http://www.rootdig.com/adn/separating_delayed_twins.html
Confusion is frustrating and on a positive note, challenging.
Michael