Debug logs are always long...
Even though you don't have that key, it shows how to do some further testing and
debuging for sudo itself.
In that article did you set the sudoers_debug to 3 - to get all info for sudo (you can
paste it here)? Did you check the nsswitch.conf for sss in it? Did you run getent
netgroup {hostgroup}?
Let me know what you get.
Aaron