Easy enough to reconcile. I see what you're getting at.
In a situation where your body is burning fat for fuel, it doesn't "care" where that fat comes from.
Yeah, if you eat a billion grams of fat, you'll be in fat burning mode but still store fat. But what's more common is that your satiety signaling will tell you you've had enough, and you'll burn the fat you eat plus get the extra energy from your body's energy storage system, the adipose tissue.
They aren't disagreeing. Yes, you can eat so much fat that you don't use any of your stored fat. But it isn't particularly easy to do in most cases. Make sense?