the pressure on the spine itself doesn't change. There is no compressive force applied to the spine. Regardless of flat back or not, you still have the same surface area directly under the bar load, specifically your upper back. When benching flat backed, only the center portion of your back takes the load, so less of your body is distributing the weight. When properly set up with the arch, shoulderblades pinched, traps retracted, you have much more body mass under the bar, which distributes the pressure of the bar over more tissues and bones. Remember, your body is 3-dimensional, you are talking about a flat plane here. Therefore, if your back is healthy, there is no danger from benching with an arch, regardless of the popular "personal trainer" advice.
You are looking at this like a physics problem, but you are looking at it as a static 2-D scenario, when you actually have a dynamic 3-D construction. The geometry of the body constantly changes during a bench press, and so the forces on all parts of the upper body... So, in the dynamic 3-d scenario, the force moves throughout the body as the angle of the normal force created by the bench changes in relation to the position of the load. This changing force is mainly distributed throughout the upper body, but has its greatest effect on the upper back area in contact with the bench. You have a fixed surface area to work against, so the more you concentrate the mass of the body, and properly angle the joints to support the weight, the easier it is to handle the weight. The force of the bar load while benching with an arch is transmitted down the arms, through the shoulders, tot he areas of the body contacting the bench. If you are flat backed, that means the force lands on the spinal erector muscles and part of the shoulder blades. When properly set up to bench with an arch, the force will land on the spinal erectors, rear delts, traps, and most of the shoulder blades. As most of the back is soft tissue, the compressive force of the load is fairly evenly distributed amongst the whole back (think in 3-D, and think semi-fluid).