There is no requirement for advertising. And precious little requirement to "prove" anything: only a few percent of H1B visa recipients are actually checked to see whether the employers are cheating. And the rules are so fuzzy that employers often get away with cheating even when they're caught.
Over 80% of applications specify a salary in the bottom quintile of the federal government's range for the job classification (which is, itself, widely claimed to be below the actual market range. I haven't researched this myself, though).