I'm confused by your post. You talk about a charter flight, but then you say that the airlines involved are American Airlines and Aerolineas Argentinas. Are two different airlines operating a single charter flight? Or maybe you're asking about baggage allowances on both scheduled flights and charter flights?

For regular commercial flights on AA and AR, your baggage allowance is determined by each carrier's rules. Some carriers, on some routes, utilize a "piece" concept: you get to check X pieces of baggage, with each piece to weigh not more than Y pounds (or kilograms). In other cases, a carrier may utilize a "weight" concept: you get to check a total of not more than Y pounds or kilograms in total, regardless of the number of checked bags. Airlines regularly charge extra for extra bags and for overweight bags. Baggage allowances on charter flights operated by commercial carriers can differ from the allowances offered on scheduled flights.

If your charter carrier says one bag not to exceed 23 kg. with no option for extra bags or overweight bags, why would you think that they don't mean what they say, or that they care "more" about one of the limitations than the other?