William Turner (1508? - 1568), the "Naturalist Turner" mentioned above, was an Englishman who had studied medicine in Italy, and was a "natural historian". He had befriended Conrad Gessner, a Swiss naturalist, whose work Historiae animalium which he published in five volumes between 1551 and 1558 is the starting point of the modern scientific study of zoology.
Turner and his Brazilian Giants
But getting back to Turner. Did he travel to Brazil? I have not found evidence that proves he was anywhere near Brazil. Yet not only does the article shown above , say so, but also several others printed in the second half of the eighteenth century. He died before the well known English expeditions to southern South America so these were not his sources. Perhaps during his exile on the European mainland he spoke to navigators who had sailed along Brazil or read their accounts. Yet, the date given in some accounts (1610) for his remarks about the flat headed natives, are 42 years after his death. Something does not fit in here!.
But getting back to his story: his giants with the hinder part of their heads [...] flat are indeed quite remarkable. But could people with such heads really exist?
Other people with a "flat occipital bone"
Not surprisingly we find that there really is a group of people with a "flat occipital bone" (the bone at the back of your skull), the Dinaric people, which are characterized as brachymorphic . They are described as having an "extremely flat occiput" and also, as "tall statured people with average height of 172 cm, 5' 8" " and living in the Dinaric Alps (whic span parts of Croatia, Slovenia, Bosnia and Herzegovina, Serbia and Kosovo), Albania and parts of the Austrian Tyrol and Central Europe .
So, is the flat skull linked to tallness?, could the flat skulled giants mentioned by Turner be an extreme example of this trait? Perhaps yes: people suffering from Weaver Syndrome, a congenital genetic syndrome, are tall (average height of 194 cm in men - nearly 6' 3") and have "flat occiput" .
An anti-racist disclaimer
Having said all this, I do want to make it perfectly clear that I agree with the
American Anthropological Association Statement on "Race" (May 17, 1998), part of which I copy below:
it has become clear that human populations are not unambiguous, clearly demarcated, biologically distinct groups. Evidence from the analysis of genetics (e.g., DNA) indicates that most physical variation, about 94%, lies within so-called racial groups. Conventional geographic "racial" groupings differ from one another only in about 6% of their genes. This means that there is greater variation within "racial" groups than between them. In neighboring populations there is much overlapping of genes and their phenotypic (physical) expressions. Throughout history whenever different groups have come into contact, they have interbred. The continued sharing of genetic materials has maintained all of humankind as a single species.
Physical variations in any given trait tend to occur gradually rather than abruptly over geographic areas. And because physical traits are inherited independently of one another, knowing the range of one trait does not predict the presence of others. 
Furthermore the notion of "race" has had hideous consequences: Ultimately "race" as an ideology about human differences was subsequently spread to other areas of the world. It became a strategy for dividing, ranking, and controlling colonized people used by colonial powers everywhere. But it was not limited to the colonial situation. In the latter part of the 19th century it was employed by Europeans to rank one another and to justify social, economic, and political inequalities among their peoples. During World War II, the Nazis under Adolf Hitler enjoined the expanded ideology of "race" and "racial" differences and took them to a logical end: the extermination of 11 million people of "inferior races" (e.g., Jews, Gypsies, Africans, homosexuals, and so forth) and other unspeakable brutalities of the Holocaust. 
So, when I mention brachycephalic, flat occiputs, Dinaric people, etc. I am not classifying anyone in a strict "racial" niche or demeaning them, but, trying to find out if general trends shared by certain groups of people, may indicate certain links between genes and physical build, and point to eras long gone, when small bands of hunter-gatherers roamed the earth. Bands that through interbreeding may have concentrated certain traits within the group and led to a tribe of Giants.
Giants in Brazil and their link to the Patagons
This nice story of Turner's flat headed giants however does not link the Brazilian giants with Patagonia's giant Patagons, because, as I mentioned in a previous post on homo erectus in Patagonia, these were not brachycephalic but dolichocephalic.
It is a shame, because when I read Turner's story, I immediately thought that I had come across some evidence of a group of natives living along the South Atlantic coast of South America from Patagonia to the south of Brazil.
 Giants, Second essay. The Lady's monthly museum, Vernor & Hood, 1822. Vol.16, pp. 312.
 Ilse Schwidetzky, A. B. Chiarelli and Olga C. Necrasov, (1980). Physical anthropology of European populations. Mouton, pp. 285.
 Ram Nath Sharma and Rajendra Kumar Sharma, (1997). Anthropology. Atlantic Publishers & Distributors, pp. 108.
 M. Cappa, M. Maghnie, S. Loche and G. F. Bottazzo, (2009). Endocrine Involvement in Developmental Syndromes Karger, vol. 14. pp. 57.
 AAA Statement on Race
Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia2010 International Year of Biodiversity Copyright 2009-2010 by Austin Whittall ©