Again, changing the profile of the tire does not correlate to air pressure. It's like saying, if I change the paint on my car to a different color, what kind of wax should I use? That is because every car and tire are designed for a specific operating pressure. It is a very complex function of tire wear, rolling resistance, grip, sidewall strength etc.
Think of the OEM tire pressure as a baseline. When you change the pressure in the tire, you are trading one attribute for another. So let's say you are at the drag strip and you need a good launch. You can decrease the pressure in the tire to increase the contact patch and sidewall rotational give to increase traction, with a tradeoff of higher rolling resistance, decreased and uneven treadwear. However, given the circumstances the benefits outweigh the tradeoffs. Conversely, say you are driving across country and will be droning at highway speeds for 500 miles at 65 MPH. Then it's probably a good idea to increase the tire pressure and improve your gas milage because you aren't going to be taking high speed turns and really don't need the traction.
My theory on why someone would tell you to increase the tire pressure on a lower profile tire is because as you decrease the sidewall, you lower the margin of forgiveness on wear along the sidewall. When a car corners very hard, the tire will roll. If the tire does not have enough air pressure the tire can roll hard to where the sidewall can start to see some contact with the pavement. If you roll far enough, you can even roll on to the wheel or even pull the tire off of the wheel. This is very dangerous. On a tire with a large sidewall, you have more play in the tire and a larger distance of forgiveness before you get to that point. A shorter sidewall tire, has less. Take it to the extreme and imagine rubber band-like tires and imagine that car taking a hard turn. How much can the tire give before it actually rides on to the wheel? Not much. By increasing the tire pressure, I suppose the thought is to increase the sidewall stiffness (makes the wheel more rigid) and give yourself a bit of added protection on hard cornering. However, tire manufacturers already know this and stiffen the sidewall to compensate for this attribute. That is why you should stick to the factory recommended pressures because the tire is designed at that given pressure to function correctly. Again, when you deviate from these pressures you are trying to trade off one attribute at the cost of another.
Also, keep in mind all of this is at the cost of decreasing the traction performance of the tire as well. Hence why high performance cars (like F1, NASCAR) don't use low profile tires. They are more for looks but actually decrease performance.