I hit this same issue with 2.7.2, so posting in case it helps anyone else. I had two issues. One was that I had to change preferences for the editing Member Group to enable 'Can change the author name when posting channel entries', even though I am not changing the author. Second, I had to change the privileges of the original author Member Group to enable 'Can edit entries authored by others', even though it is their own record that is being edited on their behalf by the other Member Group.
Here is the code that was throwing the error for me, maybe when I have time I'll see if it's 'fixable':
if ($data['author_id'] != ee()->session->userdata('member_id') && ee()->session->userdata('group_id') != 1)
if ( ! isset($this->_cache['orig_author_id']) OR $data['author_id'] != $this->_cache['orig_author_id'])
if (ee()->session->userdata('can_assign_post_authors') != 'y')