What's considered “typical” doesn't always apply to each individual situation. Another thing in those countries, race isn't always the factor behind crimes like this, it's more about nationality, she's an American citizen, they're looking to see how much the US and Mexico government are willing to put up for her safety/release.
They wouldn't have taken the woman hostage for nothing, they clearly want money or something else of leverage in return for her release because otherwise they would've just killed her on the scene

cartels and high level gangs in Mexico kill women and children like it's nothing so
keeping her just to be keeping her wouldn't make sense.
Hell, they probably would've took all four of them hostage but I guess the other three were loaded with guns so they killed them. This may or may not be the work of cartels as there are just many high level street gangs in Mexico as well

clearly something foul was at play and I doubt all four of them just went to Mexico for cheap medicines/medical treatment.