Humm, Intersting article. I have done both when I am out wheeling. I had to learn how my rig reacts on different terrain. for the first couple of years, I never aired down. I attruibute this to having a locker and giving me traction when I needed it. Also, I have allowed myself to go after more and more difficult obstacles as I got more comfortable with my rig, and got it tuned to the stuff I normally go play in. Now that being said, I have never needed to air down in sand. I run a BFG M/T, and never saw the need for it. Of course, I am cautious about where I tread. I try to stay on hardpack, or at least make sure I have 4WD ready. I have seen many people get stuck and were able to air down some and get the tration they need.
As far as mud goes, I have just recently got more into airing down. I was very afraid of damaging a wheel or having the bead pop. Matter of fact, the one time I had a tree root go inbetween my wheel and tire, I was a full pressure. I was a bit confused how this happened. I approched that same area again(different outing), and I was aired down to 15 psi. I was able to position my rig better to miss the obstacle, due to better traction. I do not drive fast when aired down. I watch my tires as they conform to the object I am encountering(its cool to watch). As far as deep mud, well again, Im not sure if it was the tires or my locker helping me. OH, and I would probably not air down below 10psi unless I had beadlocks installed.
On the road, I stick with about 28psi. The sidewalls of my tires are stiff, so any loss of pressure is not immediatly noticed(say as with a street tire). My last set of BFG's lasted almost 70,000 miles(Installed around 115k, removed at 186k). I always check my tire wear and make sure nothing is out of whack(alignment, bearings, balljoints, ect).
Hope this helps.