The bridge on a P- or J-bass does sit very close to the rear edge. Of course the original Fender bent-metal sheet bridge design is a lot thinner on the section thats bent upwards than the rear section on most replacement cast bridges, so the gap between the bridge and the end of the body is smaller, despite the saddles being in exactly the same place.

It may only be a couple of mm extra, but the visual difference on the bridge to body-end gap is significant.