Exactly why they can't be trusted!
For other places, like Sardinia, they don't explain whether the variations (1st of a month, etc) are happening at the local level. Can the data there be trusted? We are left to draw conclusions because many gaps aren't explicitly filled in.
The blue zones project limited the places they would label a blue zone to those that had good data. Many places were rejected because the data wasn't good. Looking at those places, like the UK or France, and stating they have untrustworthy data actually confirms the blue zones work of rejecting claims there due to untrustworthy data.
edit; didn't get all that was in my head out :-) So, it could be made up or support the fact that actual docs or good record keeping weren't a thing.
It's pretty strange, basically if you have a document with a bunch of numbers (say, some company's quarterly report), look at the leading digit of all the numbers. For some reason, numbers with a leading digit of 1 show up more often than those with a leading digit of 9 (i.e. 1,234,567 is more likely that 987,123).
You'd think there wouldn't be any particular pattern in the leading digit, I mean why should there be? But observational data seem to suggest a pattern.
So Benford's law can be used as a leading indicator of fraud. If you apply it to a quarterly report and there's an unusually high distribution of 8's, for example, then while you can't be certain that it's fraud, it might be flag to an inspector/regulator to take a closer look.
But when humans enter data, they tend to fake numbers with a uniform distribution - to appear more random. That's how you catch it.
Eventually, they ran out of valid SSNs for Jan 1st births in some years. (The number is on the form DDMMYY XXXYY, where XXX is assigned sequentially and YY are control digits.)
Hence, for any given date the system can accommodate 1000 people, plenty in a country with some 1000 births a week. Until you start assigning a certain date to people with unknown DOB, that is. They are now assigned a random date.
It's a particular problem in refugee communities, especially where there may be common names. No certificate, often. What happens is that the first time they need to know their birthdate is when they have interaction with a healthcare system, and the doctor (or the admin staff), when told "Oh, some time in 1931, I think", puts "1/1/1931" into the records.
All it takes is two of "Samuel Goldstein, born 1/1/1931" in the same suburb and you've got a serious risk of misidentification when one of them has a heart attack and turns up in an ambulance. Misidentification of patients might be relatively uncommon, but the danger when it happens is severe.
Here's an example of how a similar principle can be used to observe electoral fraud: https://en.wikipedia.org/wiki/2011_Russian_legislative_elect...