If the source image is 16:9 widescreen then there are no need for black bars, but if it is 2.35:1 then even on a 16:9 set (which is about 1.77:1) then obviously black bars would need to be displayed on the 16:9 TV or the picture would be all stretched.

So effectively before the anamorphic DVD is encoded the 2.35 image has black bars added to it to make it fill a 16:9 (1.77:1) screen.

If it wasn't an anamorphic DVD (i.e. letterbox) it would have much larger black bars added to the 2.35:1 picture to make it fill a 4:3 (1.33:1) screen.