I think they are implying that it could be fraud, but since there are birth certificates available, you couldn’t commit this fraud by simply making up a birth date. So a fraudulent supercentenarian would likely have assumed the identity of someone older, perhaps to claim a pension earlier.

As for the correlations, low incomes would provide a motive for age pension fraud. Short life expectancy being correlated with more supercentenarians suggests it’s not because people in those areas are naturally healthier.

Yes, they are saying that fraud is a more likely explanation for the phenomenon of blue zones.