There is something to this, but the key thing about it is diligence and knowledge. Most beginners would probably not do too well with this approach; it takes time to realize that you're due for a water change, when to drop a bag of GFO or GAC into the sump, how often you need to clean your skimmer, etc...
But it very much is possible to do this. My 20g nano was set up 15 years ago in 2004. It's lit by 2 power compact high-output fluorescents, and for the first 11 years was topped off by hand and dosed by hand. There were no reactors, and the skimmer was a classic but wholly ineffective Tunze type like the one on Julian Sprung's nano from the 1980s, and the circulation was provided by the Hydor click-monsters. I did finally "modernize" it a little with a Tunze ATO, a Reef Octopus skimmer, and a couple of Tunze 6040 circulation pumps, but it's still dosed by hand. Grows stony corals like weeds.
But, and there's a big "but" coming - up until 8 months ago I was having to cut a couple of types of acropora and a couple of types of branching montipora out of it at least every 2 weeks to keep them from overgrowing the tank. It had been that way for years - an LFS was the beneficiary. Work overwhelmed me about 8 months ago, and I neglected the tank for about 4 months, with just adding RODI to the ATO and the occasional dosing of Ca & Alk. That did not work out well for the acropora, so I no longer have those two strains. One of the monti strains also crashed, though fortunately I had some of it in another tank. The orange branching monti that I've had since 2004 got almost completely wiped out. In fact, I thought it was completely gone until I got on top of the maintenance of the tank around Christmas; to my amazement, some dozen tiny spots of it had survived, and are now growing into colonies.
During this same period, my "high tech" tank with reactors, ATO, dosing pumps and a tank controller suffered the same neglect, yet I didn't lose anything. Granted, even this tank is doing far better after I got on top of the work schedule and resumed paying close attention to it.
So the bottom line is that you can absolutely keep a beautiful tank almost completely manually. If you're diligent with water changes, you can even go without a skimmer as I did when I started the hobby in 1990. But it's a lot of work, and there really is a reason to have gadgets on the tank - they're not an excuse to neglect paying attention and performing maintenance, but they do give you a margin of error that you don't have when doing everything manually. Moreover, to keep an SPS tank manually, you need a bit of an "aragonite thumb"; specifically, you need lots of time in front of the tank, know how to interpret the appearance of the coral, inverts and fish, and know how to correct things when they start going South.