It's not based on assumptions. Many employers have clauses in their employment contracts that guarantee comparable raises along with any changes to minimum wage. And as someone else pointed out, people making above minimum wage won't be content to stay at the same level if the minimum wage catches up to them.

If your flawed logic worked, then at some point with a minimum wage raise, poverty should have disappeared from America for a period until the evil corporations let the bottom salary fall behind the curve again.