The 90% number isn't a certainty, or applicable across the board, but that's not the point of the question, and the truth certainly is that indigenous North and South Americans experienced devastation at the hands of introduced disease. I'd like to point you to this post by u/anthropology_nerd. I'd also encourage reading the entirety of the brilliant series it is one part of.

One of the many points made in that series is that the terrible effects of European diseases on Native populations in the Americas must be understood in the context of colonization efforts, warfare, and disruption on a grand scale. It is not simply the case that disease alone (subtext: inevitably) wiped out Native peoples and societies. I'd look back to the mentioned post and its siblings for further detail and multiple sources.

With this in mind, let's talk about why (as far as we know) Eurasian diseases didn't take hold in the Americas before Columbus.

Viking contact with Native Americans was simply nowhere near as intense as the European-Native American contact that would come about in the early 16th century. The encounters were "tentative, marked by confusion and misapprehension and marred by violence...[and] also ephemeral, a far cry from the apocalyptic transformation that would occur after Columbus’s voyages led to wide scale European colonization"^(1). Most Viking/Native American meetings in North America were short (and often violent) events that were not conducive to the spread of disease. The archaeological site of L'Anse aux Meadows, which was the most intensive site of Viking activity, was "a small, short-lived way station." Here's a description of the site:

The Norse have the strongest material representation at the site, but archaeological and paleoecological evidence suggests that they spent at most a few years at L’Anse aux Meadows. Their settlement was a small way station for boat repair. The pollen record indicates no massive impacts on vegetation and perhaps none at all. Although disturbance may be implied by the behavior of the herbaceous taxa, these do not include the European weeds that accompanied Norse settlers to Greenland, and there are no signs of grazing or extensive forest clearance.^(2)

Even the data from articles that argue for relatively higher amounts of Norse presence at L'Anse aux Meadows "does not imply a continuous occupation, which, given the shallow cultural deposits, seems unlikely. Rather, it indicates the possibility of sporadic Norse activity beyond the early 11th century." The same article agrees with my second source when it writes:

The paucity of material culture and shallow deposits indicate a transitory place functioning as a base for exploration of North America. Although the Norse colonization of the North Atlantic is often viewed as a search for farmland, it was also an endeavor to secure luxury resources for European markets. From this perspective, perhaps a Norse outpost makes perfect sense. LAM is located on the shores of a rich cod fishery—which, 6 centuries later, was home to hundreds of seasonal French fishers—and in a dense nesting region for eiders. Both stockfish (dried cod) and eiderdown were highly prized commodities in the Viking Age. ^(3')

So Norse and Native Americans really weren't interacting with each other that much, especially in ways that might encourage the spread of disease. This is less true for indigenous peoples who lived in the Canadian Arctic and especially Greenland, such as the Thule.^(4) But research about Norse/Native American contact in those areas - where native peoples may have carved likenesses of Vikings - still suggests "it is quite possible that such contact [was] without lasting or profound effect upon the ideas or behavior of either party."^(5) And there is "no evidence of matrilineal gene flow between Dorset or Thule groups with neighboring Norse (Vikings) populations settling in the Arctic around 1000 years ago".^(6) So even in Greenland, there probably wasn't enough interaction to create high likelihoods for disease transfer.

As for disease coming from the Basque, there is no clear evidence that Basque fishermen encountered Native American peoples or even set foot in North America before Columbus' time. The earliest accepted date of Basque knowledge of North America is from 1497.^(7)

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^(1)Cleaves,Wallace Thomas,,II. (2017). Towards a native medieval: Shared themes of visionaries, tricksters, resisters and contact between the literature of the middle ages and the indigenous traditions of north america (Order No. 10286611). Available from Ethnic NewsWatch; ProQuest Dissertations & Theses Global. (1960631096).

^(2) Davis, A.M., McAndrews, J.H. and Wallace, B.L. (1988), Paleoenvironment and the archaeological record at the L'Anse Aux Meadows Site, Newfoundland. Geoarchaeology, 3: 53-64.

^(3) Kristensen, T., & Curtis, J. (2012). Late Holocene Hunter-Gatherers at L'Anse aux Meadows and the Dynamics of Bird and Mammal Hunting in Newfoundland. Arctic Anthropology, 49(1), 68-87.

^(4) Park, Robert W. "Contact between the Norse Vikings and the Dorset culture in Arctic Canada." Antiquity, vol. 82, no. 315, 2008, p. 189+.

^(5) Sabo, D., & Sabo, G. (1978). A Possible Thule Carving of a Viking from Baffin Island, N.W.T. Canadian Journal of Archaeology / Journal Canadien D’Archéologie, (2), 33-42.

^(6) Raghavan, M., DeGiorgio, M., Albrechtsen, A., Moltke, I., Skoglund, P., Korneliussen, T., . . . Willerslev, E. (2014). The genetic prehistory of the New World Arctic. Science, 345(6200), 1020-1020.

^(7) Escribano-Ruiz S., Azkarate A. (2015) Basque Fisheries in Eastern Canada, a Special Case of Cultural Encounter in the Colonizing of North America. In: Funari P., Senatore M. (eds) Archaeology of Culture Contact and Colonialism in Spanish and Portuguese America. Springer, Cham.