I’ve installed nagios several times, and each time I follow the docs. There are very few holes/problems in the entire doc. You have found the only one that I am aware of.
The docs do show the ./configure as luca pointed out. But really, all of those are not needed if you want the default install, which is most likely all you really need.
EX, --prefix will be /usr/loca/nagios by default
–with-nagios-user will be nagios and so on. I see no reason to change any of those.
The permissions on the files installed will be nagios.nagios. If they are not, then something went wrong or you specified that the nagios user should be root.