S.G.
I have not used barkeepers friend but have been hearing about it. I have used CLR. If you have a plastic tray, you can fill it with water and CLR and let the rack sit in it overnight. It is not the stainless steel that is rusting. If it were, there would be nothing left. What you are seeing is brown spot build up from minerals in the water and only regular cleaning will help. WD-40 is another thing you can use. You can find more instructions at
http://www.zojila.com/shop/product-care-i-10.html