I used to keep my tank with the chemical/no water change approach, with a very similar setup to the tank in question (rugf and a h.o.t. filter). It worked great for a while, the fish were all growing rapidly, the ph was never off by more than a point or so, and the water was sparkling clear. People were constantly complimenting me on how beautiful it was......
Then it crashed. All of my fish died within a 2 day timespan. I had never heard of testing for nitrates in the water, and I never tested anything but ph until the fish started dying. I tested for ammonia and it was off the color chart that came with the kit, some insane number. It was like someone poured a bottle of windex in there.... I had "left well enough alone" and my fish died, poisoned by their own wastes. It took about a year and a half for this to happen to my tank....
I have since taken the hands-off approach to the other extreme...I change about 40% of the water about once a week or so, and NEVER add any chemicals to it except a dechlorinator (unless I have a sick fish, but even then I try to treat with natural methods if I can). It has served me well, and there is only one chemical bottle (stress coat) in my cabinet (besides my test kit, which is kept elsewhere...). It's much safer for me, my tank, and my other pets, in my opinion.
I think that there are as many methods to fishkeeping as there are hobbyists, and whatever works, works. Just keep in mind that it might only be a temporary balance, and any little thing (such as one potted plant dying, which triggered my tank-death) might crash the system out. I think this applies to all tanks, not just the "unique" approaches to the hobby. Aquatic ecosystems are probably the most difficult to mimic, and nothing can completely replicate them. Mother nature has yet to divulge that secret to us....