As it has been said, a properly prepared Remington will shoot just as accurate as a custom, if that term is described by the ability to shoot small groups.
But Competitive Benchrest has evolved over the years. Agging capability is the all important factor, that being described as a "combinations" ability to lay down groups over an entire aggragate that when averaged, will be the winning formula.
Often that has nothing to do with shooting extremely small groups. More times than not it has to do with not shooting any overly large groups.
When I first started shooting Benchrest, the trend was still to hunt and pick conditions. As time passed, more and more shooters started to adopt the style that is predicated on waiting untill a steady light condition appears, and then get five shots down range. Most top shooters have the ability to watch and if there are slight increases in the condition, they can hold accordingly. This takes a lot of skill, and the utmost confidence in ones equipment.
Simply put, with the advent of precisionly smooth customs, the Remingtons simply cannot keep up.