You and many Americans. Helpfully aided in that belief by TV programs like Beyond Borders where US authorities act as the World Police jumping into other countries and taking over investigations and rescuing US citizens from any and every scrape they get themselves into.

Outside your own country, your local authorities have very little ability to do much and certainly won't help you in any relatively minor scrapes (nor in most major ones either). Although the US exerts more external influence than it really should, that's limited to guarding US interests (like copyright protection or drug related things).

Unless you happen to be key to US national interest, you'll be on your own, apart from a visit in prison from the embassy staff to let you know that they know you're there - just like the citizens of every other country, as Andrew Nõmm found out.