The law that bans false or misleading advertising is the

FTC Act is the act that bans false or misleading advertising

Explanation:

The FTC Act prohibits unfair or deceptive advertising in any medium in that it is made to enforce that there cannot be false advertising of something by a product or any consumerist market thing that cannot do what it says it would do.

The law needs to be strict to decrease market fraud specially in free market economies that are as consumerist as the US where there are too many products on sale.

This is the need to be very strict by this law.