I recommend changing eating habits first. The reason I recommend this is because diet is infinately more important in seeing fat loss results than exercise. Results give motivation, and motivation makes you want to not only stick with it, but push yourself further and harder. Plus, once you've lost a bit of weight, exercise is easier to do. This in of itself is motivating.
On the other hand, if you are one of those people who can't stand diets and would prefer to exercise, it might be easier for you to start that way. However, I think the general consensus (well, at least for me!) is that nothing is more uncomfortable, gross, and boring than exercise
. At the very least, I think most people have an equal tolerance for caloric restriction as they do exercise so it just makes sense to start with whatever yeilds the best results.
I think the trainer is making the assumption that people would prefer to do exercise, and therefore one should "ease themselves into better health" by doing the easiest thing first. This assumption is not true,
especially among those who are very heavy. Like I said, I think most people have a lower tolerance for exercise than they do dieting, plus exercise yeilds smaller results than dieting. I don't see the benefits of doing it that guy's way, other than if you happen to be the sort of person who likes exercise (in which case you probably don't have a weight problem anyway ;D).