I'm afraid you still don't get it.
Rereading the paragraph below, it is clear that the non-citizen would be eligible to receive benefits "even on unauthorized work" which is a euphemism for "illegal alien working in the US without authorization".
"For example, a non-citizen retired or disabled worker may receive payments outside the United States (including benefits based on unauthorized work in the United States) if he/she is a citizen of a country that has a social insurance system that pays benefits to eligible U.S. citizens residing outside that country, which Mexico does."
So, not only would the spouse and children of the illegal alien be eligible, but so would the illegal alien himself.
This proposal is a direct assault on the US taxpayer which will force us to fund Mexican national citizens.
Now, I pinged you on another thread (Nine unauthorized workers busted at defense plant) that discussed a raid ICE conducted to arrest "unauthorized workers" at a defense plant and the ICE agent's usage of the term, "unauthorized worker" is unambiguous.
It means "illegal alien working in the US without authorization".
Which is the same thing it means in the Totalization with Mexico proposal.
No, Social Security doesn't "authorize" retirement payments for illegal work! When the Social Security Admin refers to "unauthorized" work or time, it is talking about pre-treaty efforts by *legal* workers that didn't qualify under the old rules for pension credit.
5 Legislative Days Left Until The AWB Expires