MONTREAL -- Quebec remains the COVID-19 epicenter in Canada, with over 103,000 cases here so far, and double the number of total reported deaths as in Ontario.

But as Quebec Premier François Legault delivered dire warnings about the need to respect lockdown rules going into winter, he also suggested Thursday that Quebec is doing better than it looks.

On Twitter, Legault shared a study about the number of cremations in Ontario. The study shows that the rate of cremations in that province rose sharply, with no apparent explanation, in March—suggesting there were excess deaths that should have been attributed to COVID-19.

When asked about the study, Legault said he wanted to point out that Quebec takes the opposite approach, erring on the side of overestimating, and not just when it comes to COVID-19.

“Quebec has the reputation of putting more [rather] than less,” he said.

“It's true for all sickness. I remember the study of the deaths after the weather being too hot,” he said, referring to the 2018 heat wave.

In that case, Quebec recorded dozens of deaths due to the heat wave, while Ontario recorded zero—while it was struck by the same extreme heat. 

Public health experts later said the difference comes down to how the provinces noted cause of death: Quebec counted all sorts of heat-related deaths of people with underlying conditions, while Ontario only counted people who officially died of heat stroke.

Quebec’s Director of Public Health, Dr. Horacio Arruda, put his weight behind Legault’s theory on Thursday and added some more detail.

“Anytime, in Quebec, someone dies from cancer or another disease, if they have COVID-19 it will be counted as COVID-19,” said Arruda.

“That’s not necessarily the case everywhere.” 

But the Toronto-based epidemiologist who tweeted the study—who Legault had retweeted—wrote on Thursday night that he took issue with Legault’s conclusion. 

“If you're reading my tweets, Premier,” David Fisman wrote, before switching to French, “I suggest that you conduct your own study on excess mortality in Quebec.”

Fisman, who is based at the University of Toronto, suggested the data would need to be studied in much greater detail to make a real comparison between the provinces.

“Unfortunately, excess mortality will exceed the covid deaths enumerated in most jurisdictions,” he wrote.

“So if you want to do interprovincial comparisons, ‘apples to apples,’ please, not ‘apples to oranges.’”

Fisman told CTV News that the cremation study was a good step forward because it "puts us, finally, in a position to talk about all-cause mortality in Ontario."

The more information, the better, he said -- and that goes for all provinces.

"Transparency is great," said Fisman. "Tell people how many died with COVID, how many COVID-attributable deaths you have, how many excess deaths you have."