I dunno what you disagree with but here's tha actual truth:
1)For stopping a bike on dry roads, a front brake is best; incomparably better than skidding the rear.
2)Now that that's out of the way, here goes for icy roads etc: Fixed will work even if the rim is iced over and everything is packed with snow, and you get a very fine feel for what your rear wheel is doing. So you run less of a risk of wiping out because you don't notice that your rear wheel is skidding (could happen with a caliper brake). I think that feathering the front brake and backpedaling is the best (not that I ride a lot in the winter...)