Running the command:
# drush core-config
and selecting #1 (tried them all - where #1 is selected from:  : /etc/php5/cli/php.ini )
I get back
sh: /etc/php5/cli/php.ini: Permission denied
Debian Linux (6)
After reviewing the code for a bit, I found in "function drush_core_cron()"
... drush_shell_exec_interactive('$EDITOR %s ' ...
The reference to $EDITOR assumes that there is a valid editor of choice.
So, with a non-existent bash variable 'EDITOR', it fails with the Permission denied.
Add the 'EDITOR' variable in one of your .bashrc, .profile, etc... files, fixes the problem.
I would recommend a validation of the $EDITOR variable in the code and provide a more informative message.
I will look into providing that patch in the near future.
This is documentation only.