Basically ee has it's own internal database. So I believe 'ee site info' just reports from that. So if you change anything without using ee commands then ee won't know about those changes.
But it's the include files that make stuff happen. So when you create or update a site ee decides which include files to use, and sets these at the site level (i.e. /etc/nginx/sites-available/yoursite.com). ee doesn't intend you to make any changes 'manually'.
To prove to yourself what version of php that site is using, you can always just create a phpinfo script in htdocs for that site.