radsrh, your probably are referring to a rear exit stove. For Gators application, his stove pipe exits on top of the unit making the rear of the stove itself closest to combustibles. Since his stove is closer to combustibles than his stove pipe, he can run a single wall stove pipe right out of the unit and allow all the heat to be utilized in the exterior of the cabin instead of sending out the cabin. With that in mind, he appears to have converted as he entered into the ceiling mounted box you can see in the pic. That particular component has it's own built-in setbacks to combustables in it's design. There probably is a flange at the bottom of that box that adapts his entering single wall to double or triple wall while passing through the ceiling, attic, roof structure.
On a rear exit stove, the stove pipe is closest to the wall, more so than the stove it self so that is the first set back that has to be satisfied hence the need for double or triple wall. There is absolutely no need to run a double wall pipe on a stove that exits on top, you loose the radiant heat of the pipe and the cost is like 5 times more. At some point you will need to transfer over to a different pipe to pass through ceilings as setback to combustables HAS to be followed.
All these setbacks are for safety. If you had a freestanding unit in the middle of a room and therefor far far away from combustables you could run a single wall pipe on a rear exit unit and enjoy all the heat from the stove and the pipe.
Here is my application.
I have single wall out of the top of the stove, even the elbow is single wall. The fat horizontal pipe is class A triple wall. That is required passing through the wall cavity where combustibles are an issue. There is a small adapter piece that allows me to convert from single wall to triple wall. It is an added cost for that part but still much cheaper than double wall all the way and I still get more heat radiating through single wall.