I would agree with this thought generally as it certainly happened when I started running, but in the days of just getting my steps in, my use of MyFitnessPal showed that I was eating the same diet with essentially no change to the average daily caloric intake. I did increase my water intake.
Part of this might also be about how exercise generally leaves you feeling pretty good, usually better than after a day that is spent entirely sedentary in my experience. A lot of people crave the instant satiating feeling of eating. Eating often feels good. The exercise might then help by replacing the "make me feel better" feeling that food might give you, leading to you swapping out "unnecessary" feeding and lowering your caloric intake in the process.