It turns out that the high-end stainless steel fridges actually have ferrous metal components that enable the use of magnets. It's only the mid-tier stainless steel ones that are non-magnetic. (Source: research for a product launched last year which includes a fridge-mountable magnetic remote)
Those don't fit an iPad, and if you try to make it fit, you'll invalidate the warranty. You'll have to buy the special ones that fit iPads, at the Apple store. 50 dollars. Per strip.