Psychologists / counsellors who are also qualified medical practitioners are a tiny (minute IME) minority, hence my reference to psychiatrists, some of whom will do the "talk therapies" normally associated with psychologists / counsellors as well as attending to the medicinal / medical needs of their clients.The costs of attending such a psychiatrist are included in the Revenue list under "Doctors and consultants fees".
The list, while I concede that it does not specifically exclude counsellors / psychologists (but does specifically include Educational Psychologists) is headed "Health Expenses includes the cost of:". Therefore, IME, what is not specifically included is excluded. The example you quote is also listed as an exception and thus I don't believe it makes for a good case.
From OP's point of view there is a higher probability that their diagnosing doctor can find a suitable psychiatrist more easily than a medically qualified counsellor, FWIW.