It is possible to have a US bank account for non resident. You just have to find a reliable offshore US bank account company that will handle your acc. There are lot of scammers out there in the net. Some will sell you only kits(Beware!) but some will sell you a real bank account.
You are right, bank account for non resident in USA is very much possible and all you have to need for opening an account there in USA is A copy of your passport, Electricity Bill with the address of your residential, Corporate bank accounts , and a Bank reference letter .
This question has already been dealt with in a previous thread and I would like to repeat: Recent US legislation now DISALLOW opening of new non-resident US bank accounts. Beware of any companies offering such services as they are clearly trying to get around existing laws.