Actually it is backed by US law and the strength of the US government in terms of enforcing those laws. In particular, the dollar is backed by US tax and debt

Actually it is backed by US law and the strength of the US government in terms of enforcing those laws. In particular, the dollar is backed by US tax and debt laws; US taxes must be paid in dollars, debts in the US can be cleared with dollars, and US courts deal only in dollars when working out damages or in bankruptcy proceedings. As long as people doing business in the US follow those laws, which ultimately requires them to respect the government's ability to enforce the law, demand for dollars will exist and thus the dollar has value. So it is not really about reputation or violence being used against those who would "interfere" with the dollar (whatever that means). I would argue that the value of the Yen is more influenced by reputation than that of the dollar, since people tend to treat Yen as a "safe haven" during economic crises (but ultimately the Yen's value primarily follows from the Japanese government's ability to enforce its laws).