That might be true now, I remember when Steve Jobs famously dropped one of the first iPhone prototypes into a fish take and said look at those bubbles, there is to much empty space in the phone.No, it doesn't need to be 1mm across the entire device. You can see that some components are slightly taller than the others. There's room over the battery for MagSafe and it's possible that there'll be room along the bottom or top for an RFID fob antenna and chip.
It worked perfectly with my iPhone 4. I spliced the fob open and inside is just a very thin spooled wire and a tiny chip. Most of the 1mm comes from the tape used to isolate it from the other components. I didn't want to risk shorting anything.