Does anyone have an idea of what could be wrong? Is there a better approach to opening a document using a URL?

You can try this approach:

function myFunction() {
  var url = "1bmad4K86Ov1zQHiu8gbX6GpOSL9kbNGKiE3jmaJN9N8";
  var doc = DocumentApp.openById(url);
}

If you do not have access to it it will show the following error:

Exception: Action not allowed

Reference: openById()