No. Nearly all OECD countries pay for health and pension insurance through payroll taxes. So a school in France would pay employer-side payroll taxes for a teacher, which would show up as education spending. And the teacher would pay the employee-side contribution from her salary, which itself would show up as education spending. (That is to say, “national coverage” in most European countries doesn’t work how Americans think it works, which seems to be that health benefits for middle class people are paid for through income taxes on rich people. If it did work like that, you’d be right, but pretty much only Denmark does that. See: http://www.oecd.org/tax/tax-policy/taxing-wages-france.pdf. Look at France. About 25% of the total cost of an employee to an employer, such as a school, is employer-side social security taxes—the OECD’s term for payroll taxes for health and pension benefits.)

Moreover, many countries exempt teachers from the national pension scheme, just like the US. The UK, which I used as an example above, has a teacher pension system