All employee taxes are counted as part of the embedded costs, including the ones the employee pays.
No they're not. Some are incident on the employee (not counted in embedded tax costs), some are incident on employer (counted in embedded tax costs).
My question remains; You've said that someone (whoever that is) over counts/double counts taxes. Who says it and which taxes?
I think you just don't understand it all and you're mixed up.
"All employee taxes are counted as part of the embedded costs, including the ones the employee pays."
Incorrect. Imbedded costs are corporate income taxes, employER paid payroll taxes and associated compliance costs.