Unfortunately welcome to the crappy part of taking credit cards for payments. It usually seems like the banks decide to side with the customer, though in the 2 disputes we've had they both were in our favor.
Luckily 99.999% of people are good and don't dispute charges. Even though we haven't lost a dispute it is still built in to our pricing model at .1% in addition to all the other pricing factors.
It has nothing to do with Square allowing customers. That is the system no mater what company you use to accept credit cards as it is built into the banks that run the credit card networks. Square does nothing to decide if the money is kept at the vendor or returned to the customer, that is 100% in control of the card issuing bank. Square will give what info it has to the bank when a dispute happens and may ask you for more info in your disputes section of the dashboard. It isn't in Square's interest to give the money back as it costs them money too.
Best of luck in your further business. Cash only can be tough.
Yes, there is no fee for taking anything other than CC for payment. How is there a risk with cash? they can't go to their credit card company and file a dispute over a cash payment. Basically, the only risk with cash is taking counterfeit money or employee theft. Same goes with a check there is nothing that can happen other than a NSF check and that would happen with any POS system or even without a POS system.
