I very much doubt that. A charismatic enough leader could easily get way with serious murder pretty much anywhere in LATAM. Most military dictatorships in the region were WELCOMED by the population when the coups took place. Drop a few bombs here and there, blame on some terrorist, and if you are convincing enough, the crowd will applaud as the rule of law and civil liberties are flushed down the toilet. You have some serious misconception or idealizations about LATAM.
A charismatic enough leader can get away with many things far beyond the borders of LatAm, maybe not mass-murder, but there are many ways of being violent. Arguably, obligating people to support a street rally under the threat of losing their job, income and food for their families is a form of violence... may not threaten directly
their life, but it does threaten liberty, pursuit of happiness, and the lives of their families.
The association between these governments' "popularity" and the level of violence employed by their supporters may have
correlation but this doesn't imply
causality (i.e., governments didn't act violently just because people would allow it, they did when they had no intelligent choice left). The main reasons people were tolerant of these regimes were fear (which relies not on extreme physical violence, it suffices to have people fearing for their subsistence), ignorance of these governments' actions (think pre-internet, where media control was much easier), and also expectations (the fact that some measure of violence was necessary for them to get into power in the first place makes it bearable for people to see some degree of violence as a possibly necessary evil). I would say that the level of violence used by these governments actually escalated as popular support wore down, transforming
voluntary popular support into
"holy-crap-I-have-no-choice" popular support. At some point, popular tolerance was broken and these governments lost outright support, even of those masses who depended on the government for their subsistence.
There should not be a need to label LatAm as a region of blind, heartless, absolutely stupid people who have nothing better to do but cheer for an Uzi-wielding murderous government (Romans pretty much covered the quota for that segment, except for the anachronistic Uzi part). I respect your inside knowledge of the problem, but generalizing goes a bit far. In Panama, Noriega was popular across some population segments, doesn't mean people loved him, they just had no true feasible choice and were afraid of the alternative. Serious misconceptions can go both ways.