It seems their actual policy is "the policy of Primary Local Usage":
"Under this policy, the English Google Earth client displays the primary, common, local name(s) given to a body of water by the sovereign nations that border it. If all bordering countries agree on the name, then the common single name is displayed (e.g. "Caribbean Sea" in English, "Mar Caribe" in Spanish, etc.). But if different countries dispute the proper name for a body of water, our policy is to display both names, with each label placed closer to the country or countries that use it."
Which basically means "multiple names until all bordering countries agree on the same name", if I'm not mistaken
The problem here is that the "primary, common, local" name used in a country sometimes conflicts with what specific government institutions in those countries may "officially" use.
In the situation with the Gulf, it's unambiguously true that the "primary, common, local" name used in the US by English-speaking Americans is "Gulf of Mexico", but they decided to adhere to an artificial name change declared by a political figure, whose authority to make that "official" only extends to a single branch of a single level of government.