Attempts to set up SFTP on an appliance and a new remote device (a server) failed even though all permissions look correct :
The $HOME/.ssh/authorized_keys file existed and had relevant read/write permissions (i.e. 6--) and ownership USER: USERGROUP. 
The permissions and ownership on the appliance's /loglogic/logapp/.ssh directory and id_dsa and id_dsa.pub files were correct.
In addition, the appliance could use SFTP to other remote devices.

User access at the remote device was limited to their home directory: $HOME. 

Reviewing the /etc/ssh/sshd_config may be necessary to confirm a configuration that specifies a different authorized_keys filename than the default. For example, instead of the default of:
#AuthorizedKeysFile     .ssh/authorized_keys
the setting may be configured to be:
AuthorizedKeysFile     .ssh/authorized_keys.%u
Here, the .%u indicates that the user's name should be appended to the authorized_keys filename.