Yes, I had noticed that as well. jmercer wasn't quite correct. We can reattach severed nerves. However, the limb never functions quite as well.
The nerve you see in severed limbs with the naked eye is not like a single electrical wire. It is more like a conduit containing thousands of microscopic wires. To make matters worse, even if you were somehow able to connect each one of these wires back to its severed end perfectly, it still wouldn't work, because when a nerve is severed, it's long "strands" - called axons - die, and sometimes the whole cell dies. All the connecting strands would have to grow back perfectly, and any dead cells would have to be regenerated. Most of the nerve strands are in little tubes, so if the nerve cell is still alive, the nerve can grow back down those, but you would still have to connect every single one perfectly.
The spinal cord is several orders of magnitude more complex, because not only are there millions of nerve axons travelling up and down it, there are millions of nerve cell bodies as well. Each of these would have to be reconnected and regrown.
And that's just trying to reconnect your own spinal cord. Imagine trying to connect you to someone else's, whose pathways are just a little different, different number of nerves, different number of cell bodies.
I personally think it will take nanotech to make it practical.