Identify the incorrect association of an organism and its relevant information.

The association of Balantidium coli being common within the United States is incorrect because Balantidium coli, although it is the largest protozoan parasite found in humans, is not prevalent in the United States. It is more commonly associated with areas where there is poor sanitation and where pigs are raised, as pigs are its natural host and the source of human infections.

In contrast, the other associations are accurate. Strongyloides stercoralis can indeed cause internal autoinfection, a unique feature of its lifecycle that allows the parasite to persist in the host without the need for external reinfection. Echinococcus granulosus is related to hydatid disease, which is diagnosed through examination of cysts, often seen on imaging or in surgical specimens. Toxoplasma gondii is typically diagnosed using serological tests that measure antibodies in the blood, as it is often asymptomatic in healthy individuals and can be challenging to identify through other means.