I haven't used those green bags, but I have used cloth mesh veggie-keeper bags. There are similar things at reusablebags, I think I got mine at hankettes.com.
Basically they're just cloth bags, you put the veggies in them and moisten the cloth then put them in your fridge. I have found that my produce doesn't keep 'forever' but that it definitely keeps MUCH longer than otherwise.
They're specifically designed for greens -- leafy veggies, etc. It does an amazing job of keeping them from wilting.
I've started keeping all my produce in cloth and mesh bags (from reusablebags but there are other sources too), organic cotton as much as possible. It definitely has made a difference.