The paragraph that your employer showed you does not apply to a repayment in the same year that you received the severance. Note that it refers to "wages paid in error in the prior year." You cannot claim a deduction or credit on your tax return when the repayment is in the same year. The employer should simply adjust your W-2 as if the unused severance had never been paid, and you should pay back only the net amount that you received. Your employer recovers the tax that was withheld by amending their payroll tax filing. This is a routine adjustment.
Obviously someone in the company you work for does not understand how this should be handled. You can ask them to consult their accountant or their payroll service. If they refuse to make the correction, you might have to ask a tax professional or a tax lawyer to contact them on your behalf.
