After watching many gun shops and "gunsmiths" mount scopes and bore sight them, I would rather just do it myself. They usually half-***** the job.
A couple of things I don't do that the video shows; level off the mount and level off the turret/caps. The mounting holes may not be lined up or straight with the bore. Turrets/caps may be slightly off as well, or the reticle canted inside the scope.
You may get really close or maybe even spot on but the way most company QC is I won't trust them.
I want the reticle as close to straight with the bore as possible, so I level off the action rails and after mounting the scope I use a straight edge to insure the reticle is level as well. This involves a line with a weight on the end of it hanging from a tree or, lucky me, I have a fence post that is perfectly straight and level looking out the back door from the kitchen table.
The ring lapping is up to you, I have never felt the need with a good set of rings. Another way to get around that is by using the Burris Zee rings as mentioned earlier. One of the many pluses with those rings. Unless the scope is moving I don't see how lapping rings will make your setup more accurate. The biggest problem I see is guys torquing the rings down on the scope. This can damage the scope, both outside and in.
After mounting everything I take it out back to my 100 yard bench and check how true the adjustments are and that the reticle moves straight up-down-left-right.