This is one of those, “It’s-technically-right-but-still-wrong” type things. If dietary fat is the primary source of your calorie intake (like, say you’re in a state of ketosis) then yes, your body will primarily use ‘fat’ as it’s go-to fuel source; ergo, your body is ‘burning fat’ because you’re eating more fat.
However: ‘Fat-burning’ does not equate to ‘body fat’ burning.
Your body is constantly storing and burning fat in a day, and it’s the long term balance – over weeks – that will dictate whether you’re losing or gaining body fat.
If the amount of fat you burn stays the same as the amount of fat you store over the long term: body fat remains the same.
If the amount of fat you burn over an extended period is less than the amount you store, you’ll lose fat.
If the amount of fat you store exceeds the amount of fat you burn, you’ll gain fat.
This is referred to as ‘fat balance’ and is, surprise surprise, dictated by your total calorie intake. So if you’re pouring heaps of butter on everything in the hopes of losing body fat – sorry to break it to you, but you’re fucking up.