We’re all living longer, but Mediterraneans live longest in EU, says Eurostat

you have to hide the bodies of your deceased ones

From whom? There are people living alone who die in their homes and aren't discovered for months, even years. If you have a caretaker and you pass away (and the caretaker relies on your pension to pay their bills) it is trivial to just... not say anything and keep collecting the pension. In a system suffering administrative decay, wherein the elderly are already obfuscated and ignored, there are few real means of physically validating whether an individual is alive or dead.

Low natality plays a more important factor, it’s hard for people to die young, if there aren’t many young people anymore.

True, but you can weight for natality in your statistics already. The "Blue Zone" hypothesis focuses on the parts of the population already older than 60, typically with an eye towards people who are lifelong residents. That much of the methodology is sound.