I heard this statement in Inception for the first time. Then a personal experience made me believe that this could actually be true. And recently, I came to learn about phantom limbs having pain. See this- youtube.com

It is true. At least from my own personal experience and experimentation. I have years training in the martial arts, and have come across several individuals who simply do not respond to pain the same way normal people do. It's not that they don't feel the pain. The know its there and can tell you it hurts a little, bad or really bad. But they just dont respond to it. Strange birds.

I came across the following links:
newscientist.com
and
health.com
But the real quest is if the mind really controls pain, can we not relieve people suffering from chronic backaches or arthritic pains by somehow 'fooling' the mind like in the case of phantom limbs?

I don't think you would want to "fool" the mind at all. If we break down pain, there are many reasons why it occurs. Granted inflammation can cause "pain" and can actually be a source of it. There is always a root cause though. I am a big proponent of "natural healing" and have researched and written many topics on the issue. I am always very skeptical of people who want to train you to accept pain instead of dealing with the source of it. Ergo, you can "get used" to just about anything with the right mental training, but why would you ignore an achy back any more than an open wound? We have been trained to think one is not as important as the other because we don't seem to be in immediate danger.