contact area X contact pressure X coefficient of friction = grip (traction)
The coefficient of friction is not static and falls off slightly as contact pressure increases, so doubling the contact pressure doesn't quite double the available traction. Increasing the pressure per square inch due to a smaller contact patch will result in less grip than the same weight spread over a larger contact patch. Just the opposite of what you are saying.
Going beyond rubber to surface adhesion, in most off-road stiuations, traction is more dependent on mechanical grip. Mechanical grip depends on the rubber interlocking with a rough surface at the micro level, plus tread edges interlocking with the terrain and the tire carcass wrapping around rocks at the macro level for maximum traction. In this respect, a wider tire at low pressure is almost always superior. The exception already stated being shallow mud (and snow).