Maybe newer high end Mazda 6's have this, but I doubt our poor mans 3's will.

I've mostly seen this on Mercedes, when you lock the car, the mirrors fold in.

 

Hi, it shows the button in the owners book, the picy shows the foor window buttons, the square mirror adjuster with the switch in the middle, then the round button. The book say's, with the ignition on, press the button to fold the mirrors in.

 

im guessing that its the mirror itself not the whole outside case, thats the only thing i can think of

 

Your manual may be referring to a model of higher status than your 2.0. I'm guessing that what you are looking at only comes as a premium option for the premium trim model and the "button" you are seeing is a dummy, as you already suspect.
Though we do have base, medium and premium trim/option packages here in the US, none of the outside mirrors here are power folding. They are all manual folding types. My guess is that is what you have.
We also do not have a headlight washing or wiping system available, even as a premium option, while you probably have it (washing) as std (litigated) equipment.