I think you misunderstand my point on the “who pays Revenue” point, as I believe it is quite important. Revenue won’t address this issue by way of assessment on the employee. They’ll go to the employer, mainly because it is the employer who has the fiduciary responsibility to deduct and remit the tax, and it was their error, not the employee's, but also because that is how the relevant legislation prescribes it.
Section 985 TCA 1997 provides the basic PAYE obligation on an employer to deduct tax on the payment of emoluments.
Section 985A TCA 1997 provides for the application of the PAYE system to perquisites / BIK.
Section 986 TCA 1997 provides for the making of regulations inter alia "for rendering persons who are required to make any such deduction or repayment, in the case of a deduction (whether or not made), accountable for the amount of the tax and liable to pay that amount to the Revenue Commissioners".
Regulation 28 of the now revoked PAYE Regulations (Income Tax (Employments) (Consolidated) Regulations, 2001 [S.I. No. 559 of 2001]) provides that:
"Within 14 days from the end of every income tax month the employer shall remit to the Collector-General the total of -
(a) all amounts of tax which the employer was liable under these regulations to deduct from emoluments paid by the employer during that income tax month..."
I could continue to quote more provisions and Regs, but the bottom line is that the employer is on the hook for the liability in the first instance.
There is provision for the employee to be assessed on the BIK as emoluments, and for the tax borne by the employer (to the extent that it hasn't been made good to them by the employee), to be treated as a further emolument of the employee, but I have never seen this applied in reality.
After all of that, it is a legal matter as to whether the employer has recourse to the employee for the tax - I don't know the answer to that. The OP says they drew attention to the matter and were told that BIK was being deducted, so (at risk of straying beyond my sphere of competence) would they not have a legitimate expectation that the matter was being properly addressed by payroll..?