4.7" is the screen diagonal. The total height, including the top and bottom border is listed as 5.44". This is according to Apple. http://www.apple.com/iphone-6/specs/
This seems unlikely, as cell phones are generally rectangular and have flat screens.
EDIT: maybe you could try drawing a screen with a 5.44" height and 4.7" diagonal. Euclid will not be your friend.
I think you and the parent are confusing the display size with phone size. The phone height is >5 inches. The display is 4.7 inches diagonally. The device size diagonally will be more than device height.