Problem with BT accounts and API calls- why am I getting "Parameter [brandId] is invalid" errors?

We have a RingCentral integration for CRM system we make. The integration has been used by multiple customers for few years so far, without any major issues.

Recently, a customer of us came up with an issue. The integration would not accept his password (we use Password Flow). After some investigation, we see that the customer has a British Telecom account. Basically, everything looks like normal RingCentral, but with BT branding. And when trying to authenticate the user via API, we receive the following error

{   "errors" : [
      {
         "parameters" : [
            {
               "parameterValue" : "7710",
               "parameterName" : "brandId"
            }
         ],
         "errorCode" : "OAU-101",
         "message" : "Parameter [brandId] is invalid"
      }
   ],
   "error" : "invalid_client",
   "error_description" : "Parameter [brandId] is invalid"
}

BT provides its own desktop app - BT Cloud Phone. Again, looks very similar, but with BT branding. BT Cloud Phone happily accepts that customer's password, but refuses to work with our RingCentral account that works fine with RingCentral Softphone (as well as our integration).

Is there a way to make the API work for both accounts?