How does decalcifying work, and is it something I need?
There is no relationship between tank sediment and pipe calcification. Unless he was able to show you how your pipes are actually constricted, such as where they connect to the water heater, there is no way anyone can know there is such a problem.

Unless you were shown obvious evidence of build up, this sounds like a complete scam to me from what little information you've provided. I would never call these people again.

AFAIK, calcium build up only occurs where very hard water is exposed to air, it does not build up inside of pipes. You may recall seeing elaborate calcium formations near commercial hot springs built up over decades by spraying hard water out of a small pipe. Despite the huge build up outside, the pipe continues to flow without evidence of obstruction after decades of use.