It sounds like you don't understand the basics of payroll tax.

The SS tax that gets deducted from your paycheck is only half the amount. Employers are required to pay the other half.

If you're self-employed, you pay both halves, and that is one of the penalties of being treated as self employed.

That's just an accounting/presentation gimmick. Mathematically, it would be the same if the deduction was 0% or 100% shown in paycheck, instead of 50%.

So you're saying it's fair to say employers pay payroll tax?