In order to insure normal service operations, the site administrator and the operators of a computer system have access to the entire system. The upshot of this is that computer sites have to trust the people in charge. These people can do anything on the system, including delete or create or read files, reroute mail, edit the log files, etc. Their system privileges allow them to investigate further if they think there is a need.
Most sites are VERY careful about who receives system privileges.
Many sites will go so far as to pull system privileges away from anybody they suspect of wrongdoing, even without proof. Other sites just assume that this risk is a necessary evil, and don't worry about the people in charge. We get a lot of students cheating here, so we keep close tabs on what they do. When we saw that Joe's account had a usage pattern much different than everyone else in his class, we went in to see what he was up to. Doing accounting for a private company Keeping records on every Zork game ever played editing a paper for the Bestiality study group writing love letters to his girl friend writing love letters to his dog use of the machine for other than class of your choice and we deleted the files and tossed him off of our machine.