Letter from Director ie yourself to Employer ie yourself stating you can work remotely and specifically from Thailand. State your duties and that you will not be working with Thais or Thai organisations. Seems to be what others have put.
Those are bank rules. Not immigration who would have no sight of that. The agent I mentioned to you earlier said open another account here with TTB. Need residence certificate and other normal docs etc.
Totally agree it's is strange. I spoke to an agent about an extension (Not DTV) in Chiang Mai 2 weeks ago. She said they would like a local bank account in Chiang Mai rather than my Bangkok or Pattaya accounts. No logic or rationale behind it