Apparently the reason for this is that the same part of the brain and the same processes used to model the outside world are also used when modelling the inside world of dreams.
I'm fairly convinced this isn't true. Very different areas of the brain are involved real life versus dreams, even if the sensations in a dream mimic the sensations in real life does NOT mean they are created by the same areas of the brain. Dreams mainly draw from past memories/subconscious thoughts and scrambles um all up then presents them through your sensory lobes of the brain. This is the exact reverse of what happens in real life where your experiences enter through the sensory lobes and eventually settle in the conscious thought/subconscious/memory lobes of the brain.

By the way, with the pain thing, i've never actually felt pain in a dream, extreme anxiety or fear... even to the point that they might be considered painful, yes, but never pain itself. For example i would see myself opening the microwave door, putting the paperclip on the safety switch, and putting my hand in then pressing start, it would cause extreme anxiety, but i would only wake up instead of feeling pain while asleep, i honestly don't think i would feel pain in a dream because of the simple subconscious option of just waking up. However, this might be just me though, and i'm not basing anything off of this.