All taxes, hidden or not, have to ultimately = all expenditures.
Unless there is a large underground market for health care services (not captured by national accounds because it is illegal), somehow paid for by taxation, hidden or not, your concerns seem irrelevant.
Imagine a doctor working under the table, not reporting his taxable income, but somehow still getting reimbursed by the Ministry of Health.
Right, so show me all sources of taxation in Europe that go towards healthcare. You haven’t done this yet. I understand the European government might not want the population to know, but it is what is being done.
Math is math.