Fair enough, but the parent was quoting their total payment (not just payroll) as 8% of their income, which is still an extreme underpayment, and equivalent to the case where they are only paying sales taxes.

That doesn't mean "yup, close the border", but we should still be careful about distinguishing the issues: yes, immigration may be below the optimal level, but it doesn't follow that illegal immigration is unproblematic in this respect.