It may just be me, but it feels like they write that too casually and then tweet it out and it becomes a "reality". Most people are idiots who do the bare minimum when it comes to information. So mere tweets become gospel.
It is entirely possible and likely that some people who died weren't tested (there is a shortage of tests pretty much everywhere), there are various stories of different nursing homes where they have had 3x more deaths than in previous years. I have read and heard these sorts of stories where some died and weren't tested. Was this done to hide anything? Not really I don't think.
They just write this:
In Italy, authorities have conceded that their coronavirus death toll did not include those who had died at home or in nursing homes. Similarly in France, officials have said that only those who died in hospitals had been recorded as pandemic-related — a practice they said would change in the coming days.
The Italian health authorities give a press conference every day and from what I understand, they are asked tough questions. The Italians would be talking about it themselves... Their death rate is what? 10%... incredibly higher than some other countries. Spain at 7.4 last I checked...
Ironically, Spain and Italy in particular (their media) have challenged Germany's death rate... Italians have disputed Germany's numbers and France's numbers. Precisely because there is a sense that the Italians have actually been "generous" in the way they catalogue their deaths (some say that some other countries aren't as 'free' attributing the cause of death to covid19 when people have multiple underlying conditions*).
I won't dismiss the chance that countries may mask the reality of some things, more so to not bring morale down (I feel they are constantly masking reality with regards to the lack of protection equipment and testing for instance), but I find it a bit unlikely when it comes to Italy that they've hidden numers or masked reality.
Even if you concede that loads of people who have died over the past few months may have been infected and weren't tested, it won't really change the global panorama that we are already well aware.
*Number of comorbidities - Official Italian report

For what it's worth, this is an Italian article that is saying that their "death rate" could "be lower" --- think that those testes usually have symptoms and at advanced stages many times. More likely to die. The real numbers of infected (they estimate 530K here) is much higher... and many more people survive. So they do that math and their '10%' death rate drops down.
Coronavirus, that's why lethality could be up to ten times lower
https://www.nogeoingegneria.com/news/coronavirus-ecco-perche-la-letalita-potrebbe-essere-fino-a-dieci-volte-piu-bassa/".Spoiler:
Put this article on google translate, it has relevant ideas
https://www.ilgiornale.it/news/cronache/covid-19-qual-vera-letalit-risposte-dello-studio-dellispi-1846817.html.































