If it gives bonuses to two elements, it should gives all bonuses it gives to each of those two elements.
I think I agree...but since that's what the bracelet appears to be doing, I'm not certain I understand.
Where does it say that you can't do that?
YS278:
"All bonuses of an item always apply to all of the types on the item: you can't have +2 complexity for necromancy and +1 complexity for wards in the same focus item, because the +2 complexity should apply to both..." Basically, a given focus item can only have one bonus value. It's either +1 or +2 but not both. Which is why multiplying that number by the number of element types is the focus slot cost.
It's one of several sections in the book which would have been clearer as a list instead of prose.