To add to Janet's point, the purpose of using those lower-fat products is the increase in protein. Take my usual brand of full-fat yogurt compared to 0% Greek yogurt, 3/4 c each:
Full fat: 10 g fat, 7 g carb, 6 g protein
0% Gr: 0 g fat, 4 g carb, 17 g protein
It's a better carb bargain, and I'd have to eat 3x as much of the FF yogurt to get the same amount of protein. I find the 0% just as filling, if not more.
I know satiety is subjective, and a lot of folks (myself included, at first) would think, "but if it's low fat, I'll be starving." Not so, if you're prioritizing protein. I'm not even getting as much as Dr Ted suggests, and I'm too full after my meals.
The other thought that turned me off was how it tends to be true that a lot of lower-fat products are boosted with junky starches, sugars and fillers - again, not universally true. I have to read labels carefully. That usual brand of full-fat yogurt I buy? The full-fat only contains cream, milk and cultures... but their 0% yogurt isn't the strained Greek variety and it's full of carby crap.
I buy Liberte or my store's brand.