... Along those lines; we are expressly forbidden to pour any beer at festivals. We can be there and talk but we must have volunteers who pour the beer and the volunteers are signed on with the company who runs the festival.
You nailed it there. The company who runs the festival is taking care of the insurance at that point. There are a lot of festivals around here where brewers or a brewery's employees are doing the pouring at their own booths.
And wiley hit on the subtle differences between the insurance types. In our area, the dram shop insurance is to specifically cover serving folks alcohol in the tasting room and any sort of liabilities that may arise from that (they run over someone in the parking lot and are underinsured, etc.) Product liability insurance covers the instance that someone takes one of our bottles home and something bad happens. In our case since we (will) have a tasting room and a retail sales operation, we need to cover both contingencies.
Distributing or self-distributing won't determine if you need those types of insurance; it depends on what your setup is (can people have samples at the brewery?) and if you have direct-to-public sales. You could self-distribute only kegs to bars and not need any sort of product liability or dram shop insurance, at least in our state.