Yes shoes go rusty - on or off the horse. The reason the flat edge of the shoe in contact with the grounds still looks silver is because the oxidised iron - rust - rubs off. So the edges of the shoe and any bit in contact with the hoof where there is space for air will rust and the rust will not rub off. The stud holes will also rust and if you put metal stud keepers in for more than about 24 hours they will rust in place - which is very annoying.
If a pattern on rust builds up on parts of the outside flat part of the shoe and not on others it would indicate that that part of the shoe is not in contact with the ground for some reason. Perhaps the shoe is not entirely flat or perhaps there is a deeper problem in gait or farriery which needs to be looked at.
If the whole bottom of the shoe goes rusty with no evidence of any rust being rubbed away I could only conclude that the horse has not stood on anything hard enough. No tarmac perhaps? Perhaps on box rest or in soft fields without stones? It would be unusual but certainly not impossible.