"If losing a second is twice as likely on a quad, why on earth would losing only one on a twin be so traumatic"
First, when you lose an engine on a 747, you lose 25% of available thrust, normal electrical generating capacity, and bleed air supply, vs 50% in a 767.
Second, if you lose a second engine in a 747, the airplane can still remain airborne in controlled, powered flight; where a 767 becomes an oversized glider.