Error: Could not stat() command file ‘/var/lib/nagios3/rw/nagios.cmd’!

Here's a viable solution on my debian server:

dpkg-statoverride --update --add nagios www-data 2710 /var/lib/nagios3/rw
dpkg-statoverride --update --add nagios nagios 751 /var/lib/nagios3

And... et voilà!

The proper permissions have been set and everything should work as expected

Regards