Part of the reason for the confusion is that this is a retcon of sorts. ECS was first described (with a different name) in a postmortem of Dungeon Siege, but as far as I'm aware, the modern usage of "system" was coined by Adam Martin during the development of Operation Flashpoint: Dragon Rising.

There are good technical arguments for making systems into first-class values, of course, but this interpretation will always be in competition with the older one.