Winchester put barrel bands on their early rimfire match rifles just like Springfield M1903 30 caliber target rifles had. They thought that was the way it was supposed to be made. 'Twas finally stopped on their later Model 52's and they shot much better that way.
Over the years, top competitive shooters learned that nothing should touch the barrel except the receiver; no bands, tuning screws, shims, worms or anything else between the barrel and fore end. The reason is that when a sling's attached, using it in position tends to bend the fore end a tiny bit changing its pressure on the barrel. That makes the barrel vibrate/whip different for each shot 'cause nobody holds a rifle with the same forces and position for each shot. So, make sure the barrel's free floating.
The receiver doesn't need to be pillar bedded; conventional bedding is just fine. Anschutz rimfire match rifles came without bedding; just bare metal to wood around the receiver. Torquing the stock screws to somewhere between 20 and 30 inch pounds is about right. Pillar bedding came about because the first synthetic stocs had cores in the receiver area too soft to withstand stock screw torque at this level and higher. Wood stocks never had this problem. The most accurate rifles I know of have all been conventional epoxy bedding; no pillars needed.
