Free Gift with purchase

I was at an event recently and was approached by a salesman trying to get me to purchase the product he was selling. He offered me a free gift if I made a $20 purchase.

Since when is a gift called a free gift? Is there such a thing as a paid gift? I've noticed and I suspect you have as well that in many ads a free gift is offered with purchase. I was always under the asumption that a gift was a gift. A material item given without the expectation of receiving someting in return.

Since there is no English grammar rule I can find for a double affirmative(like the rule for double negative) logic here would suggest there is no such thing as a free gift. So the two affirmatives cancel each other out thereby producing a negative. Which means there is no such thing as a free gift.

By the way, I did not make the purchse but received a gift anyway, an advertising keytag.