I agree with this in principle, except that looking inside won't help much. Obviously if the cords are cut through, you'll see it on the inside, but it's entirely possible for the body to be cut only one ply deep, or even only halfway through a ply so there's no damage visible on the far side.

When inspecting for cuts, you look at the far side for a quick rule out, but also look at the near (cut from) side to confirm no serious cut and rule it OK for use. Otherwise, you could be in for a surprise down the road.

BTW- just looking it appears the surface rubber was shaved back with no body damage. Glue it back in place and ride the tire.