You're correct in what backspacing is, but not the cancelling out part. Hopefully someone will correct me if I'm wrong, but here's how I see it.
Backspacing is the measurement from the wheel mounting surface (where it touches the axle/drum/rotor) to the inside edge of either the bead, or lip. I think it's the bead, but don't quote me on that. I always get them mixed up and "offset" uses the other surface.
So, you have one wheel with a width of 8 inches and a backspacing of 4.5 inches. Leaving 3.5" of wheel outside of the mounting surface.
You have a wheel with a width of 7 inches and a backspacing of 4 inches. Leaving just 3" of wheel outside the mounting surface.
The difference of the two is that half-inch that I mentioned. That 1/2" is OUTSIDE of the mounting surface, pushing the wheel and at least part of the tire outward by half an inch.
It's not much, but seems to me that right now you're counting fractions of an inch and even millimeters to get that tire tucked in.
Wheel width differences of an inch do not make a notable difference in the width of the tire at the tread. Or even much of the sidewall in fact. Usually it's wider ONLY at the bead itself. So it's more that half inch backspacing difference than it is the width of the wheel acting on the tire.
So, narrower wheel for me, along with probably a narrower tire. Maybe...
Paul