This is not true at all. Upping quality dietary fats is a great way to get to your caloric goal, especially if you're already meeting your protein and carb requirements. Not sure what you mean by adding fats would be counterproductive to burning fat. Fats have 0 affect on blood sugar, keep you full for hours, and are a great way to keep the fat burning going. Fat doesn't make you fat, excess calories make you fat. The point of carb cycling is to keep insulin low except for times when it's really needed, which adding fats does. So, don't be fat-phobic. Especially if you're not having carbs in a meal, you should be having good fats.
If you're trying to get to 2100 cals, and are currently at 1600 cals, and your protein and carb requirements are met, then you can/should certainly fill the rest with good fats to meet your caloric goal. What else would you fill them with?
That being said, adding nuts/nut butters, grass fed cheese, avocado, fattier cuts of meat like steak or ground beef, salmon, olive oil, farm raised bacon, whole eggs, are all great ways to get cals in with quality fat sources.