I'm pretty sure Starbucks, the merchant, would have to cover the costs not square as the processor. I used to work at MBNA and when there was fraud on an card the retailer was responsible.
In this case Starbucks paid for it. But something similar could happen with a Square transaction where they may be held responsible. Was just making a point that there are costly lessons to be learnt in the world of processing.
I suspect it's not quite that simple. Square has a lot of small-to-medium businesses, who's risk profile is higher; which has to have a increased risk on Square, no?