Yeah, that got me wondering.
https://en.wikipedia.org/wiki/Tuberculosis#History
[snip] Tuberculosis has existed since antiquity. The oldest unambiguously detected M. tuberculosis gives evidence of the disease in the remains of bison in Wyoming dated to around 17,000 years ago. However, whether tuberculosis originated in bovines, then transferred to humans, or whether both bovine and human tuberculosis diverged from a common ancestor, remains unclear. A comparison of the genes of M. tuberculosis complex (MTBC) in humans to MTBC in animals suggests humans did not acquire MTBC from animals during animal domestication, as researchers previously believed. Both strains of the tuberculosis bacteria share a common ancestor, which could have infected humans even before the Neolithic Revolution. Skeletal remains show some prehistoric humans (4000 BC) had TB, and researchers have found tubercular decay in the spines of Egyptian mummies dating from 3000 to 2400 BC. Genetic studies suggest the presence of TB in the Americas from about AD 100. [/snip]
I think there was already trade from the Mediterranean to South America for a long time. Herodotos wrote that they circumnavigated Africa, and in comparison Brazil is just a short hop with prevailing winds and currents to the west from Africa. I think the theory they just kept it a secret for proprietary reasons is sound. I would too. :)