You definitely don't want to be pinching the bat, this is not best practice in my opinion. People have been teaching the pinch the bate baseball style for years. The one thing we know about baseball players is that they are poor at bunting.
The coach in the OP's thread is doing it the right way. Hold the bat with your normal batting grip. Open the hands and let the bat slide down until where the fat part of the barrel starts. Wrap fingers around with both hands. This will give you better control than pinching the bat (try pinching the bat against a 62 MPH softball, it's really really hard).
On an inside pitch you will move the hands out of the way naturally. There is little risk of getting your fingers mashed. In 20 years I have not had a batter get her fingers mashed bunting this way.
Please don't teach them the baseball style pinch the bat method. Teach them best practices from the start. I have started with 10u before..
WHY is pinching the bat, for lack of a better term, not the "best practice"...other than you believe it to be so? Do we really know that baseball players are really that poor at bunting? Most attempts that I see at the pro level are successful, and are often executed by pitchers, who don't often hit well. Try getting hit on the fingers by a 62mph softball; you won't be playing again for a long while.