Is it true that Salary pay has to be at least double minimum wage?

No, some states ( like TN) has a min amount it has to be.
But it is less than double min wage

Here in Ontario, Your total income that you take home must equal at least minimum wage.

So if you work 40 hours, and you just get a flat fee of $400, that comes out to $10/hour.

However, if they give you $400 and make you wake 80 hours, then you are only making $5/hour, which is LESS then the minimum wage. So then they must give you more money to get you up to at least the minimum wage.