As a result of the proliferation of the postal forgeries, the Postal Administration took various steps to eliminate the hemorrhaging. These steps are outlined in several articles and books. Roberto Liera wrote two articles on the subject, one was published in MEXICANA in the July 1991 journal, entitled "Postal Forgeries of the 1868 Issue", and in October 1997, "Type of Mexico - It's History Set Straight". Then, in December of 1997 and January of 1998, John Heath's two part article, entitled "The 1868 Issue & the Great Postal Fraud" was printed in MEXICANA. Also, the handbook published by MEPSI entitled "Mexico, The 1868 Issue, A Specialist Handbook" by John Heath and Doug Stout provides good information about the tipos, habilitados and anotados.
The single most effective policy was invoked by the Postmaster General on August 12, 1871 and was distributed as Postal Circular #9. The circular made it illegal for stamps identified with one office's name to be used in another office. This meant that a stamp identified with the district name VERACRUZ, had to be used in Veracruz, no other office. Likewise PUEBLA, Puebla, etc.
In Mexico City, stamps identified with other offices names could be presented at the post office and the clerk would apply an "Anotado" overprint to them. This was fine for the main office, as those stamps could then be used and placed on letters. But in outer offices there were no anotado hand stamps, so they were forced to stay within the regulations. This may be the reason that the habilitado was born.
It would have been within policy for a stamp to be used in Veracruz (or other office) as long as the VERACRUZ name was affixed. So possibly, people brought stamps identified with other office's names into the post office and the clerk applied the local district name handstamp in order to make the postage valid. This procedure ended up with stamps having two office names on the face, the original office where the stamps were issued and the office where the stamps were used.
So it is probable that Veracruz and Puebla (and other offices), faced with the same shortage of 1868 stamps as Mexico City, began using the 1868 issue stamps but applied their own office name to any of the stamps presented from another office.
Notice that on the image above that the stamp has the district number and the district name of GUANAJUATO. At some point it was taken into the post office in Puebla, the clerk applied the PUEBLA office name and the stamp was used there, and can be noted by the Puebla circular cancel.