Their company is not the one doing the withholding, the payroll company is.  They stated that they pay their 3rd party payroll company the amount of the wages plus the withholdings.  This is very common.  It is how we pay as well.  Our payroll company automatically the deducts the amounts of the employee wages, the employee witholdings, and the employer taxes.  We pay all of it to our payroll company at the time of each payroll check.

  If you have an employee whose net wages are $2000 and tax withholdings are around $500, and you pay this entire $2500 to your payroll company, the payroll company has the liability.  Everything you've paid is an expense.  If you show a liability, it will never go away, because you're never going to pay that liability back as it was paid in full already.