That is not correct.
You should read the Federal Tax Code of Mexico, especially︁ Art. 9 (I)(a) Código Fiscal de la Federación (CFF).
Individuals are Mexican tax resident if︂ they have a home in Mexico. If an individual has also a home in another︃ country, it's depending where the vital interests are. The vital interests are considered to be︄ in Mexico if more than 50% of the income within one calendar year is from︅ Mexico or if the primary place of professional activities is considered to be in Mexico.︆
The Mexican Tax Code requires a "home" somewhere else, outside of Mexican territory, not a︇ "tax residency". It is absolutely not true, that you need to bring a tax certificate︈ for applying this national law. What you need to have is a permanent home established︉ in another country.
A tax residency and a certificate of tax residency in another country︊ is needed to use tax treaties. According to Art. 9 (I)(b) CFF MEXICAN CITIZENS need︋ to provide a tax certificate/ residency to end their Mexican tax residency if they move︌ to a tax haven or if they don't have a new tax residency. This does︍ not apply to foreigners. Therefore only Mexican citizens will be remaining as tax residents in︎ Mexico for the year they left Mexico and terminated the tax residency and the following️ three years, but this doesn't apply if Mexico has an information exchange agreement or a tax treaty with an information exchange clause with the new country of residence in effect. Again, this is for Mexican citizens only.
To conclude, NON-MEXICAN-CITIZENS (Foreigners) who have also a HOME established OUTSIDE MEXICO don't need a tax residency in the country where the other home is established, to be not taxed in Mexico, if their professional activities are not in Mexico and less then 50% of their income is not from Mexico, because then the requirements of vital interests are not fulfilled. And vital interests in national Mexican law︀ is only the source of income and the centre of professional activities and not the︁ duration of stay, having a home/friends/family in Mexico, etc.
What could be a problem is︂ managing a legal entity permanently from Mexico, because then it can create a tax obligation︃ if the main administration of the business or its headquarters of effective management are considered︄ to be in Mexico, Art. 9 (II) CFF. From a practical point of view this︅ is more a problem for Mexican citizens, not for Foreigners.
If the person has a︆ residency in Mexico but doesn't fulfill the requirements to be considered a resident for tax︇ purposes in Mexico, SAT will put the information they received by CRS to trash and︈ there is nothing to worry about. What should they do with it? Taxing someone they︉ can't tax? Taxing tourists and leisure-residents who bring money into the country and stabilize the︊ Mexico Pesos?
The idea behind this is, that Mexico want to be attractive for tourists︋ and leisure-residents as a (part-time) place of living, even if Mexico doesn't have as many︌ tax treaties as other countries have.
At the end, if the creator of this thread︍ live (also) in another country than Mexico and is not fulfilling the requirements to be︎ considered a Mexican tax resident, there is nothing to worry about from the Mexican side.️ I have also never heard about problems regarding Foreigners in Mexico, who receive money from other countries but don't pay taxes in Mexico. At the moment SAT is more interested in Narcos laundering money or rich Mexicans who want to hide money. Maybe SAT tries also to become more strict with all the informal employments in Mexico.
I would be more worried that the EU country of citizenship make problems because they still assume a tax residency there... Maybe that's also the reason for this question of the thread opener.