P.S. I know this is Thailand and often times laws are merely suggestions, and everything is OK until it isn't, etc, but If I opened a second bank account in the USA to deliberately NOT show income to the taxing state (IRS in this case) I would be committing tax evasion.
This may be why Thailand talks about 'worldwide income' and such, I don't know. But it is going to be very hard to prove legitimate taxable income on foreign people and Thais alike unless they implement a system like the USA has where money connected to a specific person is tracked in its entirety. I think this is a daunting task for the Thai government to do.