Only down side is that if you ever want to use the rings on another rifle or just take the rings off this action, the odds of the rings fitting again are low. To maintain alignment of the rings after lapping, pretty much makes this a permanent mod (rings shouldn't be removed from the action but scope can be).
Rings should be lapped little to none because it will change the diameter of the 'hole'. This can allow the ring halves to bottom out before clamping the scope tightly. Milling just a bit off the bottom of the mounting flange to regain clamping force doesn't really work either as the hole is now oval.
You can tell, I am not a big fan of ring lapping. I swap my scopes and rings between too many different rifles for lapping to work.
If the smith has them, get the Optilock rings. Much better solution. Will cost a few bucks more but in the long run, cheaper. The inserts will adjust for any misalignment between the rings so there are no ring marks on the tube. The best way to install a scope.
Also, the rings can be removed and reinstalled as many times as you want without fear of loosing gripping power.
Same concept has been carried on and improved by Burris through their Signature rings w/inserts.
Jerry