Here is what it says in the Fifth Section of the "Manual of Criteria and Migratory Procedures of the INM" about required documents for EITHER tourists or getting a MX visa of any type:
(Feel free to read away here - I'll save you some time, and you can read page 37 for Rentista visas, under "Requirements" in the gray shaded box:
http://www.inm.gob.mx/static/marco_juridico/pdf/manuales/03_MANUAL_DOF_29-ENE-2010.pdf )
Documents required: Passport
OR Identity and trip documents valid for Mexico.
INM's rules vary by country of origin and some foreign people must get a visa at the MX Consulate in their own country before being allowed to travel to MX. That's not the case for US citizens.
To be valid in Mexico, the foreign public documents, with the exception of a passport or identity documents, must be apostilled by the government authority of the country issuing the documents (if the country is a member of the Hague Convention of 1961), or if not, legalized by the corresponding Mexican consulate. This is the case for the following documents:
-Birth certificate
-Marriage certificate
The apostilled documents must be accompanied by a translation into Spanish.
Unless this has been superceded (which I doubt because it is dated 29 January 2010 in the Official Diary and Mexico doesn't seem to get around to updating things like this much more often that every 10 or 20 years),
YES, under these regulations, you can enter
and obtain a visa in Mexico without a passport. You might have trouble getting into the U.S. or any other country should you want to leave Mexico, but that's not the case for all people at the border as illustrated by other posters above.
My interpretation of this is that one could legally enter Mexico on a bus and get a MX visa with their apostilled birth certificate, a valid driver's license from their home country as a photo ID, or other type of public identity card- military ID, etc. and their bus ticket stub. Some types of visas will require more documentation such as university transcripts or diplomas, financial records, references, etc.
The initial person receiving documents at your local INM office might say "not without a passport", but either their supervisor or the local INM head would agree that a passport isn't necessary under their own regulations. They too look for the easy way out, which is a passport, to do their job.
Yes, it's easier to just use a passport. But not all people fit inside a neat, tidy box or want to do so. Thank God there are much fewer people or politicians in MX grumbling "There otta be a law against that" over their beers in the nearest tavern or pulqueria.
Being turned away from flights is usually due to airline policies intended to avoid huge fines to the airline if they let an undesirable fly into another country who is then turned away by the receiving country's Immigration folks.
There may be changes coming in the new Immigration/visa laws that they keep promising to issue, but like many things, seems to be mañana.
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