AmEx probably sees that SOPA will be bad for the economy. A bad economy means less profits.
Visa and MasterCard... maybe, just maybe, they understand that Bitcoin or some other cryptocurrency might succeed in the future, and SOPA might help them acuse Bitcoin websites of "counterfeiting" money.
Actually, come to think of it, that is short-sighted, because if no one can compete straight with them, they'll be more likely to try sideways strategies. Not necessarily virtual currency, but something equally different.
These companies want to process payments and collect their fees. The transactions in question are minuscule compared to their overall market. Someone comes along and tells them: Just do it this way, and you'll never end up in court. What do you think they are going to do/support?
(Plus, they / senior management are "in bed with" and/or effectively the same as senior management of many of the other SOPA/PIPA supporters.)