How Money Moves Between Banks | Correspondent Banking and Such Like
I've been meaning to point to this piece for a while, I've read it now and it actually answers the question on how banks do or don't trust each other to make and receive physical currency movements. The article covers the basic correspondent banking model, and builds on that to cover Real-Time Gross Settlement (RTGS), SWIFT messages, PayPal, CHAPS, FedWire and TARGET.
For all the talk about Derivatives and systemic risk - it's easy to forget that somehow the results of these transactions have to generate cash movements via a complex web of banking relationships which span countries and currencies. I believe access to this 'settlement web' was a sanctions tool used against Iran, and also a reason why SWIFT have established data centres in the US and Switzerland to ensure independance from political action spilling into the EU from the US.