Is the US->Mexico land border open for non-essential travels? (traveler has a French citizenship and a US lawful permanent residence)

https://www.afar.com/magazine/can-americans-visit-mexico-right-now (mirror) (2020-09-15) seems to say that anyone can enter Mexico:

According to Mexico: Per Travesías, “Mexico’s federal government has never closed its borders despite COVID-19. In fact, it’s one of the few countries that currently welcomes travelers from all over the world, without any kind of restriction or mandatory quarantine upon arrival.” Some states in Mexico have called on their federal government to tighten border restrictions as the U.S. case count has risen, reports the Washington Post.

However, https://www.dhs.gov/news/2020/09/18/fact-sheet-dhs-measures-border-limit-further-spread-coronavirus (mirror), which pertains to land borders only, seems to imply that the US->Mexico land border is only open for non-essential travels ("non-essential" being defined here (mirror)):

In order to limit the further spread of coronavirus, the U.S. has reached agreements with both Canada and Mexico to limit all non-essential travel across borders. Working closely and collaboratively, the Department of Homeland Security is part of a North American approach to stop the spread of the virus.

Given these two seemingly contradictory statements, I am confused: Is the US->Mexico (i.e., from the US to Mexico) land border open for non-essential travels?

If the citizenship matters, the traveler is a French citizen and a US lawful permanent resident.