It was an intriguing premise, but the more I delved into the film's background following a showing by BBC4 (UK), the more you realise that there are elements of fiction such as the family with whom Gregor/Mengele insinuates himself.
I thought it was a fascinating story. I think the director/writer, Puenzo, linked a tale in the present (1960) with the past (Nazi racial theory & genetic experiments) well, and it was a story about science: its bounds & limits. When does it stray into something much more sinister? It handled an awkward subject, how can one portray a Nazi war criminal in a detached manner? I thought the film worked well, when it played with our expectations. Does Mengele ever genuinely intend to help others or does the cold rational/methodological side of his scientific personality, the one that could experiment on live human beings, (in particular twins/children), always seep through especially towards the film's finale, the birth of the twins:& the fact that Mengele allows Lilith to suffer following the increased dosage suggests he will always put scientific 'progress', or his version of it, ahead of humanity.
So the film is an interesting imaginative interpretation of the facts (the subplot about the dolls, standardisation and uniformity and Lilith's father who acts as a counterbalance, protective of his daughter and of 'her uniqueness') :but I do agree with the OP that it is perhaps straying too far to say that it is a literal true story: the elements that are true are that Mengele was in Argentina (background), the trail went cold for a few months with the possibility that he was somewhere like Bariloche; the Nazi sympathisers, at the school (the bullying), the neighbouring surgery and local community probably echo the support networks that could allow Nazi war criminals to survive & stay underground.
I thought the story skilfully fused the narrative elements with known history, the story seen through the eyes initially of a child, Lilith. The forensic detail with which Mengele records facts in his notebooks hark back to his sinister background & past. I also read that Mengele would murder twins by injecting chloroform into the heart and we are reminded of the mechanical dolls with their beating hearts.
Is that a comment, too, on Mengele? A cold scientific automaton recording facts rather than a human being? The dolls (Hans Bellmer) become his grotesque vision of purity (Sonnenmensch).
Yet as Puenzo points out in one interview, it is ironic that a Nazi doctor ended up seeking refuge on a continent with people whose blood has been mixed so much.