Think about those SS stats... They would likely include:
Spouses that worked but did not invest $$s in their own name.
People who have spent their savings, possibly by giving it away or having private care in later retirement, in order to be eligible for subsidized long term care.
People that have spent their savings because they have lived a very long time (over 85) and don't need a lot.
People that put their "savings" into a fully paid off home. This one is pretty common, and now just pull SS.
People that put their savings into a savings account, under the mattress, etc, and therefore don't show any income.
People that spent money on kids' education, weddings, kids home down payments, and in turn, rely on the kids to support them now. (Also more common than I had thought).
People that only ever made <$60k a year and had little left over while raising families, yet the SS amount now is more than enough.
Maximum SS is $3k a month. If you have a spouse, you could be getting more than this. With a paid off home, this is PLENTY. IMO even $2k/month with a paid off home and medicare is plenty.