All the Commissioners felt they had the right to tell Kirk what to do - but conveniently only within the confines of the mission at hand (meaning we got little indication of the true extent of their powers). This would mesh very nicely with one particular usage of the title, one I'm also familiar with by accident of birth: the "Russian Commissioner" or Commissary, who is simply "a government official charged with oversight".
Commissaries were/are appointed for specific tasks ranging from the global and stately to the local and mundane. A typical assignment might be that of a Police Commissary (a title still used here in Finland, but also in e.g. France), basically the same as Police Commissioner. It is in Russian/Soviet use that Commissary would have seen its widest application, though. And the UFP usage appears very similar: "a person who gets the job done, by whatever means necessary", for any value of "job". The Russian Connection just gives the title an ominous echo, with all the negative overtones of political oversight. But that's again in keeping with the dramatic role of the Commissioner in Star Trek...
In theory, a Commissioner/Commissary might be appointed to command a military installation. Especially in polities where the roles of the police and the military are blurred - once again a trademark of Star Trek!
Timo Saloniemi