On some occasions, the Chinese invited the South American officers to take part in wargames. China quickly took to commercial wargames in the 1970s (despite efforts by the FBI to prevent the export of these games to China) and have continued developing them. But the Chinese are not sure how American officers play out wargame situations. Since they know many Latin American officers have studied at American war colleges and staff schools, and played American wargames with American officers, they were apparently thinking they could get some insights by working with the Latin American officers. What the Chinese didn't know was that, as American officers have discovered, the lessons taught to Latin American officers at American military schools don't always stick. Latin American military cultures are more traditional, with rank trumping everything else. The U.S., and many European military establishments, have developed cultures that encourage initiative, speaking frankly to superiors and free thinking in general. East Asian armed forces are also quite traditional, something which has long caused friction between free wheeling American commanders and their more protocol and rank obsessed South Korean counterparts.
On a more practical level, it's feared that the Chinese are seeking out Latin American officers who can be bought (not all, by any means, are "for sale") and buy information about the officers armed forces and local politics, and whatever the officer knows from trips to visit American military installations, or their work with American military advisors closer to home. This form of espionage is nothing new for the Chinese, but many of those Latin American officers developed friendships with American officers and the word quickly got back to the Pentagon about what was happening. Actually, not a lot is happening, as the Chinese have corruption and cultural difference problems in their own armed forces. But they are out there beating the bushes trying to get a better idea about how the American armed forces operate. The 1991 Gulf War made a big impression on the Chinese, and the later Afghanistan and Iraq campaigns impressed them even more. So much so that they are willing to spend millions of dollars in bribes and other expenses to try and find out what the Americans are up to and how they are doing it.
The Department of Defense is getting a little leery about working with Latin American armed forces. Corruption has always been a problem down there, and many officers have been "bought" by drug cartels or foreign governments (communist ones during the Cold War). But now the danger has moved beyond illegal drugs and the Cold War. China has been much more active diplomatically, and economically, in Latin America of late. As part of these improved relations, they have invited Latin American officers to visit China.