Composing this already since I figure people are going to get confused.
Arguments for strong biological determinism in mating structures rely on the belief that male mate control and mate diversity, paired with female single-mating and social security, supply a fitness advantage to both males and females which outmatches that available in a promiscuous female/promiscuous male structure. In these formulations the fitness advantage provided by this structure force other structures out of the population.
The key step here is the notion that these structures then became biologically enshrined. If so, it takes only a single counterexample to destroy the entire argument, because:
1) Like most evopsych arguments, biological factor explanations for mating structures rely on the fact that the structures are common;
2) The fact that the structures are common is taken as evidence that they spring from a universal biological source;
3) Any universal biological source would predate arrival in the Amazon (or any given location) by an enormous timespan, due to the timescales of allele spread;
4) If the Amazon mating systems were a product of social pressure overriding biological predisposition, and the biological factors were already present, then they cannot be strongly determinate of mating systems, only weakly determinate. Or, alternatively, the biological factors do not exist.