Your assumption here is incorrect because medical insurance premiums are subtracted from your income before income tax and before Social Security and Medicare tax. Certain other benefits are also subtracted from box 1, 3, and 5 wages, most notably, benefits provided under a “cafeteria“ plan under section 125. This includes daycare benefits, a health savings account or HSA, and a few other things. (Medical insurance premiums are also technically deducted under section 125.)
The logic of the section 125 cafeteria plan is that you agree to a reduction in salary, and your employer provides certain benefits to you in return. That is why those benefits are not subject to Social Security or Medicare tax, because they aren’t part of your salary.
Retirement contributions, on the other hand, are still considered earned income and are subject to Social Security and Medicare tax even though they may be excluded from income tax. This would include a 401(k), 403(b), and other qualified pension plans.
