For the most part it doesn't matter because at the spots where the tire is passing close to the frame/fork, it's unloaded by anything but air pressure and will be dimensionally very close regardless of pressure.
Lower pressure can slightly reduce the effective width and diameter of the tire. This will be by a small amount if any, <1mm, and on most tires it's negligible, but with Herse it could make a difference since they're known to "grow" more than most. Every factor matters when you're playing so near the limit.
Lowering the pressure will probably make the whole tire flex over locally at the contact patch a greater amount under turns and impact, at least if you go low enough. This could have some impact on reducing how much the whole wheel flexes in response to loads, which in turn could reduce the clearance needs up near the frame.
Ultimately when you're pushing tire/frame clearance to the limit, small differences start mattering more than they usually do, and it all becomes an experiment. The 3mm number is reasonable in a certain light, but it can be very badly misapplied. If it's a carbon bike being used with knobbies in messy conditions, for example, it's not necessarily enough to prevent wear to the paint and eventually the frame. Personally I think the 3mm number really only applies to fairweather conditions and riders that are willing to accept whatever consequences might come.