Tait's biological mother ended up raising Swanson instead, and Swanson's birth mother raised Tait, CBC News reported.
Norway House is made up of two northern Manitoba communities and has a population of about 5000 predominantly indigenous Cree Nation people.
It is accessible by airplane and a long indirect road linking it with Winnipeg, about 500 miles (800km) to the south.
In November, the Manitoba government said two other men who were close friends were also switched at birth in 1975, at the same Norway House Hospital. As they grew up, people noticed how they resembled each other's family more than their own.
Eric Robinson, a former Manitoba cabinet minister who is helping the men in the latest case, said there were always suspicions in the community about their parentage
"The federal government owes these people," Robinson said.
"What happened to them is criminal.
"We can live with one mistake, but two mistakes of a similar nature is not acceptable.
"We can't slough it off as being a mistake. It was a criminal act."
The former aboriginal affairs minister added he suspects there are more undiscovered cases.
"It's something (the government) can't sweep under the carpet. There are lingering questions out there," Robinson said.
"These two gentlemen are not the only victims. We have families who are deeply hurt by this. We have siblings ... that are hurt by this."
Canada's health department operates the Norway House hospital.
Canadian Health Minister Jane Philpott said the second case "deeply troubled" her, before adding an independent party will be hired to investigate hospital records and look into whether there are other such cases.
"Cases like this are an unfortunate reminder to Canadians of how urgent the need is to provide all Indigenous people with high-quality health care," Philpott said in a statement.
Canada's 1.4 million indigenous people often live in dire social and economic conditions with subpar health and education services.
Practices to ensure the identities of newborns have improved since the 1970s, and Norway House Hospital now fits infants with identification bands, the health department said in a statement.
