what about millions on welfare and medicaid
Government transfer payments are part of NIPA Personal Income, so, yes, it's counted.
The real eye opener is that theyt don't count social security taxes as savings! That is roughly 15% of your earnings (you +employer).
The 500 billion I mentioned was based on only the 6.2% for SS (of 7.65% total, the rest is Medicare) employee portion of FICA. The employer portion isn't part of NIPA Personal Income although it probably should be. If the employer half of the tax didn't exist, most of the funds would be paid as gross compensation in cash instead of being paid as a hidden (from the generally unaware and uninformed public) tax. The exception to this are the self-employed who pay the entire 12.4% for SS, so in their case both halves aren't being counted as savings.
In a world without SS and FICA taxes or in a world with a mandatory 6.2% contribution to a private account, most people would save 6.2% or more and it would all be counted as saving.
Because it is all called "taxes" and disappears into the black hole that is the current federal budget and it is all spent in the current budget year, none of it is counted.
Which is ridiculous, but all the BEA NIPA-based "savings" numbers are just the leftovers from accounting identities designed to measure other things and have never provided realistic information on savings and investment.