The essential point at issue here appears to be the tax treatment of the reimbursement of the cost of travel and taxi fares in respect of travel between home and work.
It is a long established principle of tax case law that the expenses of travelling from home to work and work to home are not expenses of travelling necessarily incurred by an employee in the performance of the duties of his/her office or employment and hence are not tax deductible. It follows from this that where the employer reimburses (directly or indirectly) the cost of travel between home and work, such reimbursement is taxable. Revenue has the same obligations as any other employer and is accordingly legally obliged to deduct tax under PAYE in respect of the cost of taxi fares paid or reimbursed and of car expenses paid.
For the sake of completeness, it should be noted that Revenue guidelines provide that the charge to tax does not arise in exceptional circumstances, e.g. where an employee is on-call to deal with certain emergencies and is called out only on an exceptional basis, or where an employee is required to work very late on an occasional basis. However, this exception could not be extended to reimbursement of expenses for travel between home and work, which is rostered, predictable and occurs on a regular basis.