So... I just spoke with clearXchange. This is what I understand of how their system is set up:
If you are registered to CXC, but your bank is not one of the seven member banks, then you can only send to one of three banks: Chase, Bank of America, or US Bank.
If instead your bank is one of the seven member banks, you can send to non-member banks.
Perhaps the next bitsquare update can include this info when you are creating national currency accounts, and make a note when you are trying to start a trade.
I just learned about this on my third attempt at a trade, because I had to call the clearXchange customer support to get an explanation of why this was happening....
So... it seems that, basically, if you want to be sure you dont have any problems when using CXC, you need a bank account with one of the three banks I mentioned above.... But I havent been able to put that to the test yet.