The Deputy will be pleased to learn that he has been misinformed. There is no such anomaly.
There is nothing in the Road Safety Authority driver test booking system which links the driving test with motor tax, so that not having motor tax, or proof of motor tax, at the time of booking is irrelevant to the test application process. The only motor tax requirement connected to the driving test is that the vehicle in which the person presents themselves to take their test must have a valid tax disc on the day of the test.
I would like to point out that people can use another vehicle – they do not have to undertake their test in their own if for some reason (tax, insurance, NCT) it is not available on the day. Many people rent the car for their test from their driving school, for example.