Seems like a strange rationale (the mere presence of a bar on premises), but I know nothing about CA hospitality law or liquor laws. I do know that hotels in many U.S. states have 21 as their minimum age. I just assumed this was a general law in those states unrelated to whether the establishment had a liquor license or stocked minibars in the rooms. (I can see a state permitting 18-year-olds to rent hotel rooms, but then having a provision that they can't have unsupervised access to an in-room minibar.)
I guess that's a long way of saying I don't doubt that you really need to be 21, but I'm not sure if the availability of liquor on premises is the reason. (Alofts don't have minibars...I know that part!!)
Frankly, there should be a maximum age of 25 to check in to an Aloft, because anybody over that age is going to hate the dormroominess of the place.