I've been on several cruises with my children and without their father. I've taken my children's friends with different last names and neither of their paretns. I"ve taken grandchildren with different last names and without their parents and have NEVER EVER even been asked about missing parents let alone any letters or documents. The last cruise I was on was last August.
The only time it mentions a missing parent letter at Carnival is if you're in Mexico more than 24 hours and none of the ships are so I'd like to know where people gather all their information from.