If you stand your brush up on the wooden handle, then the water that's in the hairs will run from the hairs into the wood. The risk with this is that the wood, as it gets wet, expands, and so can loosen the ferrule. If this happens, it means the brush hairs aren't held as tightly, so they are likely to fall out as you paint.
It's not something that's going to happen overnight though, and if you use a piece of paper towel to get most of the water out of the hairs before you wrap them in tissue (which tightens as it dries, so helps keep the shape of the brush hairs), it's likely never to be a problem.
You can buy brush holders that hang the brush by the handle without the hairs touching the surface; alternately wrap an elastic band around the brush handle and hang it from a hook, or leave them flat to dry (the handle should keep the hairs off the surface).
