The Release Notes are correct. If you control two Archives (
somehow), then all of your extra draws will be quadrupled.
When one Archive replaces a card draw, it replaces something that both Archives perceive as one action (a card draw) with
two actions. (Two card draws.) The second Archive will then apply separately to each of those two card draws, resulting in a total of four cards drawn–applying to the first one doesn't stop it from applying to the second one, because they're two separate actions.
(This is the same reason why casting Divination with only a single Archive out will get you four cards rather than three.)