Question about Assign and Append to privilege

I am curious at to how Assign and Append to privileges are used

1. When i go to an opportunity record that i own and change the owner to an user from child BU, do i need Parent-Child BU level Append to privilege for User entity?

2. When i go to custom activity that i won and change the owner to an user from child BU, do i need Parent-Child BU level Append to privilege for User entity?

Looks like with BU level Append to privilege, i am able to do #1 but not #2 and this has me confused. When exactly is Append to privilege for User entity needed?