BTW, the height dimensions for the One and SGS4 are 136.6 vs. 137.4 - the One is less than one millimeter taller.
I applied a simple rectangle to see if the photo in question passed muster.
Because of the perspective difference, I repeated it at the midpoints in an effort to give every opportunity.
Enlarge or shink on your monitor to actual size.
Not exactly less than a millimeter difference, now is it?