If people were looking, they would have noticed the deduction was 12%
The employer contribution is a fig leaf covering the truth
The notion that an employee's pay would have automatically been 6% higher absent the employer's SS contribution is quite a stretch.
More likely the amount of the employer contribution would have simply increased the employer's pre-tax income.
My memory is that self-employed paid 14%, then the ‘employer’ half was deductible, but the full amount had to be paid before taking the tax deduction.