Some of this comes from different interpretations of the role of government. Although there is separation of church and state, the Constitution recognizes our rights as inalienable and endowed by the Creator; they are not rights granted by our, or any, government.

It is of course reasonable to expect that American citizens will be held to the legal standard of the countries they visit, but there is also a natural reaction against seeing being held without charges, or being denied a 'speedy' trial, or being charged with a crime that we would see as self-defense, as 'legal' repercussions. They violate rights that Americans consider 'inalienable' - without regard to borders or governing bodies. Without commenting on that mindset being right or wrong, that's just destined to cause friction in this situation. Throw in Twitter as the main forum for these discussions and I imagine it was a wreck.

I really wasn't paying attention to people who were outraged at the situation, so I don't know what they were complaining about specifically, but I imagine the skew from our concept of American justice (which is incredibly flawed in practice, but theoretically built on strong morals) was part of it.