Not being from the world of offshore accounts (I am fortunate enought to be able to visit and dive, not deposit) I thought most "black" accounts are dealt with on a cash or proxy (diamonds, gold etc) basis to avoid any paper trail. At least that is what the Swiss banker claimed on 60 minutes.
On the other side, maybe it is a tpl account and it is used for local business expenses like office, electricity, housing, client entertainment etc etc.
Good luck
(I) C. W.