White grease has a very high melting point and won't usually melt in the hot oil, leaving it to possibly plug up the filter. Rare, but I've heard of it happening if you use tooooo much and it makes its way to the filter.
Permatex makes a great assembly lube for mains and rods. The Moly lube paste is the best for cams and has a very low melting point. On my current rebuild, it began mixing with the oil during the priming of the engine. We had the intake off and could see it blending in with the oil.