Yes, I understand exactly what you are saying. However, you need to understand that PXB is not creating the new binlog. PXB itself does not create binary logs. MySQL is creating the new binlog. Whatever permissions mysqld is running as is the permissions (owner) that the new binlog file will inherit.
chmod 777 is incorrect and a bad practice.
I see someone else had a similar issue with PXB and docker. Please look over this conversation and see if you have a similar setup.