All the actuaries in the world are not worth spit if you start with flawed assumptions and that is exactly the criticism of the SSA's projections.
The GAO is one of the very few organizations within the entire Federal Government that actually has a decent and credible track record. Somebody already posted this but apparently you missed it. Here is what they said:
In testimony on September 11, 2003, the GAO challenged the SSA’s methodology for estimating the costs of an agreement with Mexico. The methodology failed to take into account the estimated five million illegal alien Mexican workers in the United States, Mexicans now living in Mexico who earlier worked illegally in the United States, the fact that the agreement likely would make family members living in Mexico eligible for benefits that they are not currently entitled to, and the effects of a proposed new guest worker agreement. Also, the GAO found that there was no effort to systematically study the record keeping of the Mexican authorities who would be partners in the program to assure the validity of information received from that source.
In other words, the Social Security Administrations actuaries badly blew it. They left at least 5 million recipients out of their actuarial calculations.
If the illegal working in the US in 2002 under a phony SS number didn't keep his check stubs, what makes you think that the illegal worker in '92, '82,'72, '62 kept his? The further you go back in time, the less likely documentation exists.