I think I now know what the rule is, and it looks like LA/LP/AA are right.

The AA all-partner award between Zone A and Zone B specifically prohibits connections at a point located in Zone C, with several exceptions, one of them being that direct (single flt #) LP flights between SA2 and NA are allowed, even if they make a stop in LIM.

It seems then that since EZE is in SA2, and LIM in SA1, and the flight is not direct, the EZE-LIM-LAX routing has been correctly turned down.