Hi guys! Got back a delivery from Apple. Or should I say from my Swedish carrier. And guess what? They gave me a completely new phone from China. With same rattle.

And I don't really think this can even be fixed, because the design of the chassis is what it is. I am 100% assure that this thing is on EVERY 5S. But also on a 5. So You who can't live with this, simply buy another phone. You who can, You've probably bought a case as I (hello Pinlo Slice3) and have decided to live with it. It has no other "problems" than this one. And as for me, I decided to keep it. Simply because I can't find an other phone with my demands, even if Sony Xperia but also LG G2 were really close (especially Z1 which I almost bought today).
So now You know guys. There are no such thing as a "perfect phone", because that phone would had erased all others from the market long ago. Like Nokia 3210 once did. Interesting however that some users here reported no rattle what so ever, which I now strongly doubt that they had. If iPhone 5S from Australia to USA have exactly same thing (yes, I talked with some magazines and people), then everyone, yes E-V-E-R-Y-one has it. And as I thought before, Apple can't recall all 5S in the world because they can't fix them. Because, they must redesign everything and that will cost a big bunch. So that's why you can't hear any rattle from 5C or 4S and 4, and other devices because they are not designed in aluminum.
I really hope I made myself clear now, and now I know it's nothing wrong with my phone. Or Yours. Have a nice Holliday and please move on. It's a phone, not a Ferrari. ;-) Thought I never would say that... ^^