Europeans around the time of Columbus described natives of America as stark naked or in Adam's finest. Did they literally mean nude or just nude by European standards?

Not only did such societies exist, they still do, although they may not all still go fully nude. One example that immediately comes to mind is the Asmat people of Papua New Guinea, who as recently as the 1970s went fully nude most of the time, with the exception of jewelry and body paint (as documented most famously by Lorne and Lawrence Blair for their Ring of Fire book and BBC series).

As for the Americas, North and South America are huge places with incredibly diverse populations of Native people. The practice of describing precolonial cultural practices isn't always clear-cut, because it's dominated by prejudices in contemporary European accounts, revisionism in early ethnographic work (early anthropologists wanted to capture "pure" indigenous practices, which meant that they ignored aspects of culture they deemed "tainted," and they ignored some groups altogether and declared them "extinct" -- it's a major factor in why some tribes are federally recognized and some are not, and it's a major point of contention between Native communities and the fields of anthropology, archaeology, and history). Native oral histories and oral traditions can be very personal and private, and Native descriptions of their own traditions is best left to Native people, rather than academics.

With that huge caveat, I will offer, as one example, this description by Petr Kostromitinov of the Native Californians (likely Coast Miwok people) living in the area of Bodega Bay in 1839:

The men go completely naked, but the women cover the middle part of their bodies in front and in back with the hides of wild goats; the men bind their hair in a tuft on top of their heads, the women at the nape of the neck; sometimes they let it fall freely; the men fasten the bunches of hair by means of little pieces of wood rather artfully carved from a red palm.

That is one account, and it is by no means authoritative. However, if you are wondering if it is possible that there were people in the Americas who went fully nude, the answer is yes.