Sure, Square has to "live within the existing system"...in fact, from everything I've heard from them, their value-add is that while they live in it, they shield you from it.
They are very sympathetic with regard to how crappy banking technology is and try to shield you from that; however, it doesn't seem that this sympathy extends to the charge-back side of things.
They (Square) did shield him from as much of the hassle as possible. They provided pretty good support from an email perspective. And more importantly, they did NOT charge him the usual $25 fee any typical processor would charge him for the chargeback. Which I might add is charged to merchants regardless of them winning or losing a chargeback so again, Square "shielded" this guy from typical charges any business would always have in a chargeback situation.
The problem is this is "money" movement, not customer service "sympathy" issue. Square like any company moving money is as sympathetic as possible but when Square gets a chargeback notice, you are GUILTY until proven innocent. As stated multiple times elsewhere, in plain and simple language a chargeback means the card holder says they did NOT authorize the transaction which means they are saying "This is a fraudulent" transaction. If you ran square, just exactly how much sympathy will you have for any business when this happens? especially as stated, you'll have to cough up the money regardless of whether you get the money from the merchant or not. And, do all that work with no extra fee to offset the hassle and customer service for doing it. So, in the end, Square did a really good job overall from shielding this merchant from the situation.
They are very sympathetic with regard to how crappy banking technology is and try to shield you from that; however, it doesn't seem that this sympathy extends to the charge-back side of things.