A few questions:
1) how would you qualify if you don't have a social security or tax ID number?
2) if you have a social security number, you're not an illegal worker. You're, de facto, a recognized worker and are paying taxes into the system.
3) if you retain a fraudulent id number, then of course you SHOULDN'T qualify. This is what we have auditors for
4) to my knowledge, even if you do work illegally, the years worked without a valid tax id number with applicable taxes paid can't apply to the 10 year tenure required (see definition: undocumented).
5) In all fairness, I don't see why those who work legally and pay taxes, including social security, shouldn't reap some of the benefits. Depriving of such seems like it would amount to a lack of substantive due process, if not plain questionable moral practices.
Essentially, what this article suggests that if you legally work in and contribute to our society (including taxes and economy-driving labor and consumer spending), you shouldn't automatically be eligible to take part of our society's benefits. I'll acknowledge that there's an argument to be made for some circumstances. I just find the general lacking of principles of fairness to be objectionable.