Just like a 44", the 39" Bogger has a 15" tread width. A 12" wide wheel is as narrow as you want to go, no question about it. A Bogger does best with it's tread laying as flat as possible. A 44" wears alot better on a 15" wide rim and it's more stable too. With the shorter 39" the 12" wheel would be okay, but I'd still look for some 14" wide wheels. I wouldn't even consider a 9.75" wheel. People do all sorts of things, it doesn't make it right. Interco makes the tire, listen to them. For best results with a big mud tire, try to match the tread width with the rim width.
It's kind of like running a 12.5" wide tire on an 8" wheel. It works fine for a short little 33" tire, and because of that people have somehow come to the conclusion that running an 8" wide wheel is the way to go with any 12.5" tire. That's obviously a bunch of crap. Would you run a bias ply 38x12.5" TSL on an 8" wide wheel? Neither would I, and neither would any of the tire manufacturers......check their websites. Last time I looked NO manufacturer recommends an 8" wheel with a 35" and up tire, they all recommend at least an 8.5" wheel for the MINIMUM. True, that's not far from an 8" wheel......but it's still not an 8" wheel. When the manufacturers measure and spec their 12.5" tires, they are measuring them while mounted on a 10" wheel.....that should tell you something.
The inner bead that jps4jeep was talking about is called a safety bead. It's a little bulge or lip that keeps the tire from sliding inwards on the rim and coming unseated. Most 16.5" rims don't have it, and because of that the tires are more likely to pop off with hard use or severe side loading.