I don't know which project you are asking about?
But certainly in the UK, a widow's illegitimate child would normally be registered under her current surname, i.e. the surname of her dead husband, not under her maiden name. The same for the illegitimate child of a divorcee, if she has not changed her surname back to her maiden name. Just because the child has the husband's surname it does not imply that the husband was his / her father.