Sounds like B.S.
Anyone not eligible for a SSN can get a TIN and pay taxes to the IRS.
* https://www.irs.gov/tin/itin/individual-taxpayer-identificat... * https://www.nilc.org/resources/itinfaq/
And all those payments has contributed trillions of dollars https://www.cato.org/blog/cato-study-immigrants-reduced-defi...