This post was made possible by sobbayi.
There are many reasons why one may want to open a US bank account, including wanting to withdraw money from PayPal. Now to open a US based bank account as a none US resident is still possible.
The only catch is that you cannot open it online, you have to physically go into the bank with your passport and a second form of identification eg your DL (no need for social security number if you tell them you are not a resident).
You then fill the forms AT THE BANK and you set up you internet banking details right there as thats where all your transaction Bank transfers etc will take place.
Once you are done you must deposit some money into the account immediately and you will walk out with you temporary ATM card. You then need a Kenyan address and a US address. The US address is where they will send the permanent ATM card within 10 days and other documentation whenever they need to as they wont send it out of the country. Once you have your ATM card and are going back to Kenya there is a number you will need to call to activate your card to work in Kenya. Make sure you get that number before you leave the bank.
This information is based on Bank of America. (Not all banks offer accounts to non residents living abroad). Their ATM cards work just fine in Kenya but it will cost you 5 bucks ($5) per use so be careful.