News can be checked in lots of ways. If there's a factual claim about some public data, check it. If someone is assigned a job title, is that actually their job title? Does it contain internal contradictions? Does it make claims that contradict knowledge you already have, or things that were previously claimed? All those types of checks are ones I've done before to news stories and found they failed them.
Think about the NYT example I gave above. How did someone discover that their list of COVID deaths had a murder victim in it? Easy: they read the list, noticed that the 6th person was in his twenties, remembered that COVID doesn't kill such people unless they're already dying of something else and stuck his name into Google. That surfaced another news report about the murder. This is basic fact checking but the NYT didn't do it. The data was too good to check, so they didn't.
That murder victim in the C-19 data was only exposed because he was #6 in the list. Imagine if his name+age were buried on page 23/45. Checking each and every name in a list that long is beyond a reasonable standard for fact-checking for an individual journalist.
It was because he was the first non-elderly person in the list, which is an obvious thing to double check because COVID basically never kills people below a fairly high age. That was already well known at the time.
If journalists can't check the claims they're making, they shouldn't make them. The fact that the NYT wanted to make 1000 factual claims on the front page doesn't suddenly mean they don't have to check them. It means they shouldn't pull that sort of stunt. The loss of trust is clearly deserved.
Think about the NYT example I gave above. How did someone discover that their list of COVID deaths had a murder victim in it? Easy: they read the list, noticed that the 6th person was in his twenties, remembered that COVID doesn't kill such people unless they're already dying of something else and stuck his name into Google. That surfaced another news report about the murder. This is basic fact checking but the NYT didn't do it. The data was too good to check, so they didn't.