That is not what the term means. Americans traveling abroad have to follow the laws wherever they are, but they are still "subject to the jurisdiction" of the US Gov't.
If you are detained abroad, the US State Dept will endeavor to get you released, or at least try to make sure you receive a fair trial.
The meaning of the phrase (at the time of the 14th) had to do with which country had a claim over an individual. The British were stopping US merchant ships at sea, and impressing British subjects (and former subjects) into their navy. This created a lot of tension with the US, and was one of the causes of the War of 1812.
"Subject to the jurisdiction of", was how it was determined which country had a claim to (or responsibility to protect) the individual in dispute (the subject).
Diplomats still have to follow our laws, we just can't prosecute them when they don't. We can only expel them from the country.