Unfortunately for that hypothesis, the image file contains no alpha channel, and the material's opacity is set to 1.
However (!!!) my billboard object has the default Anim8or values for all the material parameters, which includes a "diffuse" value of 0.7.
And another However: I just recreated the model, with diffuse set to 1, and it makes no difference.
![Sad :(](./images/smilies/icon_sad.gif)
I guess I'll have to try creating a CMOD billboard and see what that does.
*sigh*
This evening.