No to all the above. The box I saw was a black box that looked like Slater I think. The EC on the job told me that he failed in another town because he did not have the screw there. He said the OTHER AHJ told him that it had to be installed. He said something to the effect, "When there isn't a screw there the box is only rated for 30 lbs' , but when you have the screw, it is good for 50lbs."
Now I know this other AHJ and he is a nit picker. He likes fail guys for anything that he can. He usually does his homework and finds out small details with which to fail you. However I think that sometimes he will stretch a point just to be able to give you a red sticker.
So when this EC looked to me for some guidance, I told him that I would look into it. I have seen the boxes and they do have a small hole in the top where a screw could fit through and hit the rafter. I just can't seem to find more info on the matter.
