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Assume I have a .375 S/S double. I put a low mag scope on it. I am sure I have read that you only sight the scope in for one barrel or the other but I can't for the life of me work out why. Wouldn't it be better to shoot both barrels (I assume you would get lets say 2" at 100 yds and sight the scope to the middle of the group.

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Mike,
Yes, the idea is to end up with your scoped double shooting both barrel groups to the scope.
This may or may not require a new load to be worked up for the rifle once the scope is mounted.
About the only time you would sight the scope to just one barrel is if you could not get a load to shoot both barrels to regulation after the scope had been fitted.
In that case re-regulation is another option.