Whether this is good advice will depend partly on what you replace the fatty foods you cut back on with, and how much fat you're currently consuming. And it's not entirely clear to me what level of fat consumption is ideal. That said, it sounds like she understands that calorie intake is ultimately more important than fat intake, and was not claiming eating less fat by itself was a sufficient condition for losing weight. What are you complaining about?

FWIW, research from the National Weight Loss Control Registry apparently indicates that the rare people who lose the weight and keep it off generally eat low fat diets.

Cite: http://www.nwcr.ws/Research/

My personal theory is that fat is not inherently unhealthy; it's just that if you eat a healthy diet you will naturally end up eating a diet which is low in fat compared to your typical American. In other words, I think fat is a somewhat useful proxy. But if you just focus on reducing fat intake, you will end up eating a lot of low fat potato chips and ice cream and drinking a lot of soda. Not good.