That's my understanding as well. Three stage catalytic converters reduce nitrogen oxide emissions through reduction, so it makes sense that a reducing flame (oxygen starved) would produce less nitrogen oxides than an oxidizing flame.
Measured at the downpipe with the sniffer in the lambda sensor hole it shows no (or almost no) CO and a bit more NOx than you'd really want, but after the cat there's no measurable NOx either. The tailpipe emits basically just warm carbon dioxide and water vapour.
What is the downside to this? Obviously availability and ease of filling is part of it, but any other downsides?
In theory the engine makes a bit less power flat out, but I never drive flat out. It's quieter, runs cooler and cleaner, and has a bit more low end torque because propane burns with a bigger slower bang.