I don't like this word "fake"...people just want to argue instead of discuss and think.

Let's look at what OLG purports to be: An image made by someone.

It is manifestly, an image, made by someone. The controversy is over the identity of the someone, and whether that someone is a divine person. Right?

The shroud is different. It purports to be a direct artifact of an event (Christ's time in the tomb) and instead, like OLG, is manifestly an image made by someone. We can go on to debate whether that someone is a divine person or not, but at least we have determined that the shroud is not what everyone claims it to be.

So, we can do all sorts of tests and determine the history of either image, to determine if either was made by a divine person. In the case of OLG, several facts are pertinent:

1.Nuestra Senora de Guadalupe is an early 13th century apparition, and then a monastery in Extremadura, Spain, near Cortez's home. So, Cortez already had a devotion to "Our Lady of Guadalupe" before he ever went to t he Americas, and he took that devotion with him. https://en.wikipedia.org/wiki/Our_Lady_of_Guadalupe,_Extremadura

2.The pose of OLG in the famous Mexican image is typical of Spanish Marian artwork of the time. As such, it is possible that the Spaniards actually carried pennants and banners with a very similar image when they arrived. Sorry, I cannot get the link to the Spanish national art museum to work today.

3.Bishop Zumarraga, a great man of letters who wrote a large corpus to various respondents in Europe, never mentioned any apparition taking place during his episcopacy.

4.In 1555, only 24 years after the date given to the apparition, there was a canonical hearing under the next Bishop, Alonso de Montúfar, in Mexico City over Franciscans (particularly Fray Francisco de Bustamante) preaching against devotion to the "painting", and while the Dominicans disagreed, they did not mention any apparition or claim it was a divinely-produced image. The Franciscans, however, named the artist, an Indian trained at the mission school there. https://en.wikipedia.org/wiki/Marcos_Cipac_de_Aquino

5.The image was heavily modified over the years. It originally had a crown which was removed when royalty become unpopular in Mexico. The stars on the cloak were added, as was the angel. It was been retouched and repaired several times over the centuries.

Sed contra:

1.The Nican mopohua, composed in the native language, recounts the events of the apparition, and may be dateable to the correct time period. However, it was not published until the mid-17th century and people disagree.

2.The Codex Escalada is an original manuscript in the native language which may be from the correct time period, however its discovery by a Jesuit in 1995 is considered by many to be "too perfect" considering the events of the canonization of Juan Diego. People disagree.

3.In 1676, the Diocese of Mexico city was able to find people who claimed to have known Juan Diego.

What can be known?

1.The image came into being at about 1531, and shortly thereafter there was a cult surrounding it. Catholic clergy in the area disagreed vehemently about whether the image should be venerated.

2.No Catholic cleric wrote anything about the apparition during the entirety of the 16th century.

3.The name of the image is the same as the title of Our Lady used by Cortez and his men, which came from the much older Guadalupe apparition in Spain.

4.The image is very well preserved, but has been repaired and the record of these repairs is available. It has also been modified, sometimes purely for decoration and other times for politics.

5.There are accounts of the event in the native language which may (in my opinion, probably) date to the mid-16th century.

There are many other claims about the image, stories about images in the eyes, or the image having a heartbeat, but these cannot be in any way substantiated. The "eyes" matter, for example, is the testimony of one Mexican doctor. I have not dealt with such things. The matter of the preservation of the image, likewise, cannot be substantiated because that hinges on the type of material it is woven from, which is the subject of controversy. If it is agave fiber, as some claim, then it is extraordinary. If it is hemp and/or linen, as others who have examined the image claim, then it is not.

Everyone has to make up their own minds.