This is not how mapping works internationally. There is less agreement than I think you imagine. To give a simple non-political example, how many oceans are there and what are they named?
There are myriad authorities that maintain the official database of geographic names for use within their jurisdiction. Conflicts between these various databases are common. No one has the authority, either in theory or practice, to determine what a "correct" map looks like. To accommodate this, all mapping companies maintain a huge number of deltas for each authority.
There isn't One True Map. It is really a vast number of separate maps maintained in parallel, one for each jurisdiction that claims the authority to dictate what a map should look like. To the extent possible, companies try to minimize the number of parallel maps they must maintain. Geographic boundaries, even uncontested ones, give a hint of why this is necessary. An international border is commonly shared by several administrative jurisdictions (national and then subdivisions of each nation). If one of those several jurisdictions does a high-precision survey that moves some inconsequential line a few centimeters, what gives them the authority to edit that border for every other jurisdiction that shares it? Managing these inconsistencies is one of the basic challenges of making quasi-authoritative maps.
Mexico does not have an argument here. Everyone in every country uses an opinionated map that reflects a self-interested narrative that therefore is in conflict with maps used elsewhere. This isn't a surprise or shocking, things have always worked this way. The US, like Mexico, absolutely has the authority to make any map they want. No one is required to use either of those maps and in fact many countries reject both the American and Mexican versions of the map.