I've not seen neck turning with factory chambers make accuracy worse. It is a nice way to produce both lighter and more consistent neck tension with factory dies though. The drawback in a factory chamber is that neck clearance is usually quite generous, so if you turn your necks you may now have even more, say 0.010" or more of clearance which will work the brass more with each firing cycle and shorten its life.
If your goal is to shoot 0.5MOA consistently, Id recommend high quality, match type bullets first. If that doesn't do it, then I'd try high quality brass (if you aren't already: Lapua, Peterson, ADG, Alpha), then as the final step; I'd get a new barrel. Neck turning isn't something I would put in the "shrinks large groups" category. It's more in the "creates more consistency" category.