>Heard about one guy that tried to get his Bitcoin winnings onto his regular account, his bank wouldn't accept it because they couldn't verify its source. Of course, he managed to open up an account at another bank who accepted it without question, and transferring it to his main account from that bank was also done without question, so it's not exactly consistent.

You nailed it here without noticing it: you just use the right bank(s) in the right countries, and then just shuffle and move money around.

I'm pretty sure there are organizations dedicated to set up these operations.