Earlier quoted context omitted.
Square does high enough volume to negotiate better rates than you'd expect.
Your source, or is this pure speculation? Even Walmart can't negotiate Visa/MC interchange fees.[1] And they do ~400X Square's volume. It's not just a matter of merchant/processor size. Once enough consumers have adopted it as their primary/only card, the card network has an extremely strong position. (This is why AmEx rates are more negotiable; it's usually an alternate card.) [1] They do lawsuits instead. http://ww…
First hand, I've seen a small ecommerce shop have rates lowered a 1/4 percent doing less than $1m/y.
Second hand, Costco, who in the US and Canada just switch from AmEx to Visa as their accepted card, went through long negotiations that resulted in booting Amex for not matching the discounted rates Visa was willing to offer.