When the abdominal muscles are lax, like after pregnancy or weight loss, the rectus muscle is plicated (tightened). The plication tightens the case that contains the muscles, but this case does not stop at the border of the rectus muscle. This tough casing, called fascia, is continuous around the abdominal wall. So, whenever the rectus fascia is tightened, the external oblique fascia is also tightened, and the potential for improving the waist line exists.
If the external oblique fascia remains loose after the midline tightening, then and only then is there any benefit from separate plications on the sides. This is rarely the case, and so the plication is rarely indicated. The lateral fascia is also not as thick as the midline fascia, so sometimes it will not hold a stitch well enough to provide any benefit. If there is too much fat inside the belly, further tightening is also fruitless. It's like trying to close a suitcase that is too full. It will still hurt and still has the risk of bleeding, and even small risks are not worthwhile when there is no benefit.
These considerations and many more go into the planning of every surgical procedure. I encourage you to learn your options, but the only way to determine what the best course of action is with a person consultation with a board certified plastic surgeon. This is why plastic surgery training takes so long. You cannot learn it all in a weekend course, or from Google.
The option of tightening the oblique fascia has been available in the US and everywhere else, since tummy tucks where described. By choosing a board certified plastic surgeon, you are likely to find a plastic surgeon who is well trained, and who can guide you to your optimal results by choosing the options that will work best for you, avoiding unnecessary risks.
Plastic surgery evolves slowly, and new innovations that are successful are quickly shared with our peers, and at national meetings. When you are investigating a specific procedure claiming to be new, innovative and that delivers superior results that nothing else can, please proceed with extreme caution. The mainstream plastic surgery procedures, like tummy tuck with one of the highest "worth it" ratings on Real Self, have been around a long time. Many innovative surgeons have contributed to its success, and it is difficult to radically improve the results. It will happen, but it will not be as simple as adding a few stitches on the sides.