Sure, China gaining control over SA countries is undesirable from my point of view. If, however, countries invite China to do so, that is not something that other countries can do much to prevent unless they can offer similar goods/services at a similar cost.
In cases like this Argentina didn't went directly to china in order to get the JF-17, it was a looong trip where considerations for other aircraft (Mirage F1s, M2000s, etc), all in one way or another were criticized by the Uk for including certain equipment that it was considered "Dangerous" (although the french never stopped offering them).
With a tight budget and not much options that are in the range of an LCA, the FA-50 was seen as a decent choice (a plane that at that time even lacked BVR missiles!, in no way it was a threat), but it was blocked...essentially driving the buyer towards the JF-17 or whatever Russia/China could offer.
The whole deal just revolves in the replacement of the old A-4 fleet, not in reviving tensions on the south Atlantic.
I find strange that the Argentine MoD was sent to discuss tejas, it was never seen an "official" option, i guess thats its entry to the list.