I know for a fact that’s not true because when I was in Japan I saw some wild monkeys being cared for and they specifically had signs on the all showing the family trees of the different monkeys being cared for and explaining how the families all worked

One of the things mentioned was that the grandparent/parent/child units would all work together more closely with each other than non-family members, though they were more collaborative overall than humans

Also elephants come to mind as a non primate mammal