Notice how it says its determined by g/cm, hay is pretty much the lightest material possible and would be useless for shielding. Sure anything can be used, if you had a mile of hay it might help but I doubt a few bales will do anything. Remember this is the same people that sad hiding under a desk can protect from nukes.
No, the point is not everyone is at ground zero; and once you reach a certain distance from the blast, even minor protection can help. Maybe in the case of a nuclear attack you'd prefer to stand in the open air, lamenting how nothing can be done. As for me, I'd rather take a desk over nothing and have some protection against flying glass and collapsed ceilings.
By the way, according to this site the density of hay is 160 kg per meter cubed.
http://www.fao.org/docrep/007/j4504E/j4504e08.htmWhich is only about 1/6 of that of water at 1000 kg per meter cubed. Now I can easily plug this information back into the wiki-chart (noting the fairly consistent inverse relationship of "halving thickness" and "density" in similar materials) and get a halving thickness figure of 3.75 feet, or less considering that the wood of the barn is being used as well as the hay.