There's a
huge difference between all-cause mortality numbers being wrong, and covid-19-attributed deaths being wrong.
The only way the all-cause mortality numbers can be significantly wrong is if you suddenly find piles of corpses and skeletons around, and that they belong to people who magically weren't being missed or noticed by friends, family, neighbours, etc. And the only way for governments to hide these numbers would be by digging mass graves, shoveling them full of dead bodies, and hoping no-one notices. This simply does not happen, modern countries do not get this number wrong. If there's any public statistic you can count on going back centuries, it would be the number of births and the number of deaths.
Excess mortality is simply graphing the number of deaths backwards through time, to find trend curves and spikes in the trend curves. Those numbers are as correct as the underlying numbers.
In comparison, correctly attributing a death to covid-19 is very difficult right now. Tests are in short supply, so a lot of countries aren't testing already dead people, because those tests can be better used elsewhere, to save lives. There might be political pressure to downplay the severity of covid-19, so cause of death gets fudged here and there. Cause of death is also not always straight-forward, a lot of people are dying with covid-19, not from covid-19, how should they be counted? Different countries have different rules here.
The NYTimes article is saying that a bunch of countries have unexplained excess mortality, quite a lot of it actually. And since the most likely cause of those deaths are in fact covid-19, it means that those countries are under-reporting, i.e. their numbers are garbage. In comparison to those countries, Sweden's covid-19 deaths align pretty well with Sweden's excess deaths. The official number is still probably wrong, but there's absolutely no way that Sweden's covid-19 numbers are more garbage than those other countries, and there's absolutely no way that Sweden is under-reporting to the same extent.