For some reason I kept getting this error (even when the file was readable by all) in one of the munin (mysql slave) plugins that I had written.

So this was the solution that worked for me;

under the [mysql*] section in /etc/munin/plugin-conf.d/munin-node 
I added this: 
env.mysqlopts -u{user} -p{password}

and in my plugin

I did something like this:

mysql ${mysqlopts} -e'show slave status G'

and that seemed to have picked up the user and password from env.mysqlopts and the plugin started working (ofcourse after I restarted munin).