ACZmey,
Welcome to the board... For the most part their information is correct. Having live sand will take out most of the cycle time, but you have to consider some other things. If you purchase live sand over the net, you could have some die off, which will cause a rise in ammonia, creating a cycle. It may not be a major cycle since there is already nitrifying bacteria in the sand.
Even though the nitrifying bacteria is there, there are 2 basic groups of bacteria, aerobic, and anerobic. One likes oxygen, the other does not. This is the reason for the deep sand bed. If you were to purchase live sand, and just put it in to you tank. then anerobic bacteria will need to be "deprived of oxygen" to do it's work. The 2 types of bacteria work together to remove ammonia, nitrites and nitrates. (Actually converting it, but no sense going in to exact details here.)
By having no nitrates, the hair algae does not have food to sustain it. (The article also states "no reef tank will be completely without algae", they use janitors to keep it in control, they offer the same "janitors" on this site, referred to as a clean-up crew.) The proper spectrum of lighting will also help keep hair algae from being a problem. Their basic system does work well, as long as you know/understand the basics. As far as their lighting goes, I have the same lighting and it works well for me, but there is a possibility that they may be slightly deceiving here also, but I do not know for sure since I have not asked them yet.
I read a different article than the one that you have referenced here. In it the referred to a ballast to run 3 40W bulbs. They may be using the IceCap 660 ballast to power these bulbs (2 tritons and 1 50/50 actinic in the other article). This ballast will increase the output of those bulbs to about the same output as VHO bulbs. (this may be the deceitful part...)
As LetTheirBeRock said, they do sell their homemade aragocrete™ rocks. In other articles from their site, I read that they cure their aragocrete™ rocks, I guess because of the portland cement used in them. If they are cured in saltwater, this is a plus in the fact, it is like getting pre-cured live rock.
You can do the same thing by purchasing the same materials from you local fish store, provided they offer it, and in the same time period. They really have not come up with anything new, just have made it work for them. Yes they are trying to sell you something, but in the same respect, the have given you a lot of information at no cost to you.
They have done a fair amount of research in coral propogation, and it works well. Just like this site, there is a lot of things you can learn at both places. Here you have many people in the hobby willing to share their successes and failures here. We have nothing to gain by sharing our information, except for helping our fellow reefers.
Continue to read and learn, there is much good information to be learned.
Best of luck