One does not gain "full benefits" from working 18 months.
You're quite right. The 18 mo's must be in combination with the "quarters" as shown by the Mexican equivalent.
We will be forced to accept a proven corrupt, lying, cheat government's word for their contributions and you can wager it all upon Mexico's not hesitating to "enhance" their records if it comes down to American taxpayers ending up supporting Mexican retirees and all their other "qualified" recipients.