Actually, they do. You pay half of the payroll tax and the company pays the other half. This is payroll tax and not income tax, that is Social Security and Medicaid. This is why if you're self employed, there is a self employment tax.

That said, I think that the parent is making a different point. I think the parent's point is that if the owners and employees of a company are paying taxes, then taxing the profit of a company taxes twice, once for the profit and then again for the income that comes from the dividend.