Mormon Bishop Rowlan, who heads the Stokes' Weddington church, would not say whether he would be open to naming a non-Mormon as a Scouting leader.
"I'd have to take each one on an individual basis," he said, adding that that is the policy of the Church of Jesus Christ of Latter-day Saints."
Typically, it's the Deacon's Quorom advisor. There have been isolated incidents that I'm aware of where non-mormons were leaders, but most of those were because the advisor couldn't or wouldn't act as the Scoutmaster.
The position of Scoutmaster is separate from the Young Men’s organization. Advisor’s are sometimes called as assistant scout masters, but the SM is it’s own.
I have served as a SM. I have also served as the Y M President. While the example you sited might happen if no one else is available, it’s not typical.