I don't think this follows. While the system as a whole might be eventually consistent (where consistency is defined as: what's in the General Ledger), it doesn't follow that you relax constraints on the parts.
The individual components are generally ACID and the steps to move data are ACID as well. The only thing that prevents the whole system from being ACID is that transactions don't go immediately from POS/ATMs/card clearance/cheque clearance into the General Ledger, but instead must go through a series of intermediate transactions. But those intermediate transactions must, themselves, be ACID.
That's why I talked about how the boundaries matter. The final central accounts are ACID, the subsystems are ACID and the data transfers are ACID.
edit: though to contradict myself, I expect that there will be counterexamples in different banks where some stores or steps will not be strictly ACID, but will have been "good enough" or with sufficiently-acceptable workarounds that they haven't been upgraded. I don't think this fatally breaks my argument, but YMMV.