As much as I personally hate this way of putting it, "15 times less fat" is an example of a construction that is by no means restricted to advertisers and in fact is so widely used that it can hardly be called wrong. The intent is obviously to express the opposite of "A has 15 times more fat than B" as "B has 15 times less fat than A".
Let's look at the straightforward logical meanings first.
- A has 15 times more fat than B. - If B has 1 unit of fat, then 15 times that amount is 15 units of fat. A has 15 units more fat than B's 1 unit, i.e. A has 16 units of fat.
- B has 15 times less fat than A. - If A has 1 unit of fat, then 15 times that amount is 15 units of fat. B has 15 units less fat than A's 1 unit, i.e. B has -14 units of fat. (Which clearly makes no sense.)
Now what most people actually mean.
- A has 15 times more fat than B. - For most people, this is a less clumsy way of saying "A has 15 times as much fat as B". If A has 1 unit of fat, then B has 15 times that amount, i.e. 15 units of fat.
- B has 15 times less fat than A. - For practically everyone using this construction, it is a less clumsy way of saying "B has one fifteenth the amount of fat as A". If A has 1 unit of fat, then B has 1/15 unit of fat.
"15 times more" is ambiguous, though for the number 15 there is little difference. It is particularly bad with "twice more", which for some people means three times the amount (logical interpretation) and for some means twice the amount (wide-spread colloquial interpretation).
"15 times less" is not ambiguous. Since in real life the logical interpretation almost never makes sense, this construction is not used by those who subscribe to the logical interpretations.