The claim that adobe bricks were not used until the Spanish conquest is mostly made in the context of the Southwest US. It is usually attributed to comments made in the 1890s by Jesse Walter Fewkes, an early proponent of the emerging field of anthropological archaeology. Though there had been people digging up and documenting the material remains of indigenous American societies since Thomas Jefferson, 19th-century archaeology was mostly concerned with finding fascinating objects for museums and determining if the ancestors of modern Native American built the earthen mounds of the Mississippi and Ohio river valleys. This changed with the formation of the Bureau of American Ethnology, which aimed to preserve the threatened cultures of indigenous Americans (without challenging the policies that threatened them, of course), and the development of the American School of anthropology under Franz Boas and his students, which prioritized the particular historical development of cultures. These gave birth to an anthropological archaeology that started with present day tribes and tried to extrapolate their histories with the aid of the material record. One of its most important tasks, then, was establishing chronologies in a time before stratigraphy analysis was robust.

Fewkes made the assertion regarding some adobe construction he found at the ancestral Hopi sites of Homol'ovi and at Mesa Verde. He argued that these did not represent a "tradition" of brick-making, but a temporary response to a lack of stone to fix existing walls. Since these bricks also appeared to be formed by hand, he did not count them as "real" bricks. This seemingly pedantic distinction was relevant in turn-of-the-century archaeology, however, when anything that could be used a chronological marker was used as such. Finding mold-made bricks at a site would be a handy tool to quickly identify post-contact constructions. Thus, while "bricks" would continue to be found at Homol'ovi and other sites across the Southwest, publications throughout the 20th-century generally supported Fewkes. Even one author who used tree rings to date some bricks from Aztec Ruins National Monument to between 1090 and 1110 AD insisted that they represented a failed experiment: "had the experiment which produced them not been adjudged a failure, brick-making as a source of building material [...] would soon have come into vogue."

The Homol'ovi sites were reevaluated as part of a large project by the Arizona State Museum in the 1990s. They found even more expansive use of adobe bricks at the sites, including many that were likely formed in molds, based on experimental recreations. Its seems that rather than being an "experimental" practice, it was one only used when other materials were unavailable. Indeed, nearby historic towns plundered Hopi ruins for adobe and stones given the lack of materials otherwise.

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I don't know of any other place in the Americas this claim has been made and where adobe was a common building material pre-contact. There are absolutely more obvious examples of brick usage, though. Societies on the coast of Peru used enormous amounts of clay bricks in their monumental architecture. Huaca Pucllana in downtown Lima showcases the idiosyncratic bookshelf style masonry of the Lima culture (ca. 200-700 AD). The elaborate friezes of the Moche huacas (ca. 200-500 AD) covered their interior brick structure. The sprawling Chimu city of Chan Chan (ca. 1300 AD) was also built mostly of brick.

The bricks of these sites have actually played a significant role in debates on the sociopolitical structure of the people that built the monuments. Bricks from the Moche Huaca de la Luna have unique "maker's marks", and bricks with the same marks are the same size and placed in sequential chunks. Many claim this suggests the bricks were made in local communities before being brought to the Huaca as a sort of labor tax; the marks meant communities could receive credit from the state for their work. Later sites, such as Chan Chan, do not have bricks with maker's marks, but do have more consistent sizes across the site; this may suggest the state was more directly involved in brick production at all levels. In turn, this has been used as evidence for a Moche state that ruled diverse local communities and for a centralized Chimu state that integrated those it conquered. Of course, there are others who argue it's all just bricks and you don't need state taxation for this kind of community cooperation.