Yes. I am a UK citizen, and run my US LLC from the UK. It's possible to do everything as a non resident alien, but complicated. I'll be posting more on leadthinking.com about how to get a bank/merchant account.
Does this mean that I can incorporate there and run the business with a physical presence from some other country?
Yes, but you will still pay taxes in that other country. In fact, most states other than Delaware will also not charge you income taxes if you incorporate there but not not earn money in that state.
Does this mean that I can incorporate there and run the business with a physical presence from some other country?