Advertising fraud is already illegal. The situations where case law dictates what is illegal are varied and nuanced. As a side note, there are many categories of claims that fall in neither "provably true" nor "provably untrue", and enforcing upon these claims is tricky.
You can google for "advertising fraud precedent" "advertising fraud case law" and "advertising fraud case studies" for more information.
You can google for "advertising fraud precedent" "advertising fraud case law" and "advertising fraud case studies" for more information.