I agree that the documentation is miss worded, Initialize is the wrong word.
Its more useful to setup/assign global variables. After a function returns, its local variables no longer exist. Sometimes people create libraries which use Arduino core functionality like PWM, Serial or millis().
When creating a global variable, their constructors are run before setup. So if it uses things like I mentioned above, the code using them must be setup/run after the internal init() function has run, which setup() is perfect for.
You'll notice many people make classes will init() or begin() functions which are usually for this purpose.