Most of Afflictions shirts are done in waterbase discharge but they run them through an enzyme/silicone wash afterwards. The enzyme wash exhausts any of the WB/DC ink left on the garment so that you don't feel any of the process and the silicone softeners lay a sort of cap over it all to give it a very "buttery" handfeel.
The weight of the fabric also dictates the handfeel. I like to use a 40 single jersey in my T-shirts. That's why Afflictions t-shirts feel so nice. They like to use 30 and 40 single fabric that drapes really nice and washes up really soft.
I've done hundreds of thousands of garments like this when I owned a dyehouse/washhouse here in L.A. so really nothing new. If you ever decide to do this process make sure you tell your washhouse that you want them to add a little caustic soda into the bath to lower the PH in the water in the softener cycle. The silicone softeners penetrate better at lower PH's. Also, tell them not to use pure silicone but to do a 50% regular softener and 50% silicone mixture. 100% silicone softener tends to get gummy if you leave it too long in the dryer. I used to do this exact process for American Apparel since the manager of their custom/private label department was a good friend of mine and used to send me a lot of their customers for wash/dye processing.
HELP! 
