Presumably a lot of things give the exact same benefits. The OP's post sounds like a generic description of "I'm healthier". He said he cut out sugar; he didn't say he exercised more. I'm guessing that's why he thinks the cause was the sugar.
Yes, this. My level of exercise hasn't really changed. I just didn't want to imply that I was sitting around doing nothing, and losing weight solely from the sugar. I'm sure the exercise was a huge part of that, but I definitely saw more weight loss the past month after cutting out the sugar than I did previously from the same level of activity.