My understanding is that tri-engine jetliners were actually more to fulfill a regulation than for engineering reasons. There are regulatory limits to how far a plane is allowed to fly on one engine called ETOPS - I forget what it really stands for, but the colloquial expression is: Engines Turn Or Passengers Swim. It used to be limited to around 2 hours I believe, meaning you've got a bit of time to divert and make an emergency landing. But if you're crossing the ocean, it's not really possible, so for a long time if you were crossing an ocean, you needed a 3 or 4 engined plane to do it.

Jet engines are extremely reliable however, they fail on the order of several hundred times less often than piston engines, and are very well proven and have basically only improved, and so ETOPS rules have been relaxed quite a bit meaning that a lot more ocean crossing routes are available to twinjets.