Keeping in mind I don't speak Spanish and am using Google Translate, it seems a digital photograph that was attached to the extradition request was not an original photograph, and two experts disagreed as to whether it was Hector Beltran-Leyva. Under Mexican law, Article 236 of the Federal Code of Criminal Procedure, the trial judge was required to conduct a hearing with both experts, and if they could not agree, appoint a third expert. The trial court had determined it wasn't necessary for an extradition matter. The Appeals court says he's wrong.

Here's what I think is the interesting part: The Mexican prosecutors convinced the trial court the person in the photocopy of the photograph allegedly of Hector matched his digital arrest photo by a comparison technique known as an "anthropometric measurement system" which was used in the late 19th and early 20th century. The appeals court called the system obsolete. It is right.

Here's the google translated paragraph from yesterday's order:

In this particular case, such divergence is essentially due to the fact that, for a specialist, there are not sufficient practical or scientific technical elements to carry out any kind of identification, since the digital photographs annexed to the formal request for extradition are not original, and An anthropometric record contained in the records is obsolete for these purposes, among other things. "

Here's a bulletin by J Edger Hoover explaining the system has been obsolete since 1933, based on a 1903 case.

What were prosecutors thinking? Here's an article from 2014 explaining.

The Attorney General's Office (PGR) concluded the genetic and physiognomic surveys that show that the person arrested yesterday in the state of Guanajuato corresponds to Hector Beltran Leyva H , leader of the Beltrán Leyva criminal organization.

He determined that there is morphological, dimensional, chromatic correspondence and of particular signs among the analyzed photographs.

The ministerial institution indicated that the "study is based on the anthropometric system of the human face, analytical, comparative and deductive methods as well as measurement indices, which as a whole have the purpose of recognizing the similarity of people through the Physiognomic features through morphological specifications according to size and location on the human face, chromatic comprising the color of the skin, eyes, hair and complementary specifications or particular signs.

Here is how they measured the first photo (which is a color photocopy of a photo, not even a digital photo.) Here's how they measured the second photo which appears to be a digital photo.

According to the last linked article, the prosecutor also claimed to have DNA evidence showing Hector is Hector, by a comparison of his DNA with his brothers. So I'm not sure what the problem is, unless it is that the U.S. merely submitted a color xeroxed photo of Hector in its extradition request and relied on a few cooperators to identify the person depicted as Hector. If so, he's right to raise the argument in Mexico, because his brother Alfredo made the same argument in his case in D.C. and was promptly shot down.

The Mexican appeals court sent the case back to the trial court to get a third expert. Assuming it can find one who agrees with the prosecution, a new extradition order can be entered. In the meantime, Hector will remain in prison.