In the summer of 2008, Thomas Ajamie was in Mexico City taking a deposition for his client, the Mexican affiliate of ADT Security Services Inc. Ajamie was interviewing Juan Reyes, one of ADT’s former executives. Reyes, looking nervous at times, described how over the past four years a handful of ADT executives in Mexico had been arrested and incarcerated, including himself, on charges related to a contract dispute. Reyes had reason to feel uneasy. His four-and-a-half days in a Mexican jail were a horrific experience. But there was another cause for his anxiety: The Mexican businessman, Jesus Hernandez Alcocer, who Reyes said was responsible for the arrests, was sitting just a few feet from him at the deposition table.

Throughout the litigation — which ADT had brought against Alcocer and others in Texas state court — Alcocer had regularly attended depositions of adverse witnesses, which he was allowed to do under Texas court rules. Alcocer, who is in his late 60s, was hard to miss. He wore flashy clothes and could often be overheard on his cell phone at the depositions. In Mexico City, Ajamie says, Alcocer’s wardrobe included a gun in a holster on his belt. (Alcocer’s lawyers deny that he carried a gun.)