Speaking as a French person, 15% of my pre-income-tax salary sounds close to what I pay for state-sponsored healthcare (I pay more than that, but it includes retirement contributions and stuff).

In the case of the UK where I live, approximately 20% of all government spending goes on healthcare. Taxes on businesses, retail sales, house sales, wealth, capital gains, etc all contribute to the cost of healthcare, not just income taxes. That means a lot less than 15% of anyone's individual tax is spent on it.

However, depending on how you define "socialized", lots of people are covered under several "socialized" programs by the US government, not just Tricare. Medicare (old or disabled people), Medicaid (the very poor), CHIP and things like that (poor kids). Also, if you're counting Tricare, probably any health insurance provided by any level of US government (federal, state, county, city) to government workers should count.

In the end, the US government pays for healthcare (or, at least, much of it—US prices for healthcare are very high, and the way our insurance works means that insurance is just part of how the bills get paid, though a large part) for an high percentage of our population, one way or another.