I only speak from my personal experience. In the past (pre 2001) it was possible to set up a business bank account in the USA if you weren't a US resident (I opened one back in 2000 which I now wish I didn't close in 2005). I tried again in 2012 and it proved impossible due to the changes in the KYC regulations. If SVB and Stripe have figured out how to get around the KYC regulations I wish they would share their knowledge with the greater startup community.

I am sure Toyota opened their accounts pre-2001 so I am not sure they are the best example.