It isn’t totally false; the claim that the use of the generic masculine is the result of or may have been informed by sexism is based on the fact that it hasn’t always been that way.

Here is a more nuanced and better take:

The generic masculine in modern English is a recent development, as you noted: English used the non-gendered “they” for groups of people and hypothetical/non-specific individuals until prescriptive efforts arose to make it more like Latin. (You can find lots of traces of these prescriptive efforts in modern English: “don’t split infinitives” and “don’t strand prepositions” are similar rules imposed to make English more like Latin, which are still taught in schools but most people don’t really follow.)

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