Honestly unless it has to do with medical history, I don't even know why it should matter on most of those forms...peel off everyone's skin, and we all look exactly the same. Medically, some ethnicities are more prone to certain diseases so I get that, but why does it matter to the guy at the bank when I'm filling out an application for a loan?
I agree, ethnicity is much better to say than race. It's much more applicable to what is trying to be described, and it's way less polarizing than saying "race" these days. Everyone is so sensitive about the racial aspects of everything, I think that it actually detracts from meaningful discussion a lot of times.