What they are selling is basically what my grandmother used to call a girdle. They call it something else these days because that's such an outdated term. It seems like a great idea.
But what people are after, which does look healthier is a more solid core, the band of muscles from thighs to chest, including your abs, back and chest. Core muscles are very important in stabilizing your body and forming a foundation for building the rest of your musculature. Shoulders, legs, arms all need the core to be stable and solid to work hard and effectively. Your posture, which also affects your breathing starts with strong midsection.
A solid, lean core is a good indicator of risk of cardiovascular disease and heart attack also. We've all heard of visceral or belly fat. That fat (which you generally can't spot reduce) is a major health indicator. Insurance companies and health professionals look at the ratio between belly and hip size, and many tout it as more important than the oft quoted BMI or body mass index. The reason is that BMI doesn't take into account muscle vs fat so heavier people with a lot of muscle might appear obese compared with a lighter person who has little muscle. This is misleading. OTOH, if your waist is too big it indicates increased risk of diabetes and heart disease.
A WHR of 0.7 for women and 0.9 for men have been shown to correlate strongly with general health and fertility. Women within the 0.7 range have optimal levels of estrogen and are less susceptible to major diseases such as diabetes, cardiovascular disorders and ovarian cancers. Men with WHRs around 0.9, similarly, have been shown to be more healthy and fertile with less prostate cancer and testicular cancer
There are some good exercises for core strength in P90x Core Synergystics. For example, a lot of push-up exercises and stabilizing or balance exercises help with core strength. For instance, balance pushups, where you reach up with one arm then under does this. Core/Syn has dozens of these and it's intense! Traditional squats and deadlifts also focus on these areas. Skiing-specific exercises including many plyometric and balance exercises also help the core.
Another one I use for skiing is press/lunge. In this exercise you stand with your feet together, press two dumbbells overhead of a moderately heavy weight and then do a lunge forward on one leg (or backward) and then back up. Repeat 10 times for each leg. This will get your abs, legs, shoulders and arms.
But the point is, you want to look healthy in your middle and it's important to your health too - don't buy a girdle - you need to work on your core!