Wow, that's right! "Mato" here refers to grass that is not mowed or well-tended. I didn't even notice the analogy, lol. Just as a curiosity, there is a Brazilian state called Mato Grosso, which translates to "Thick Forest" or "Thick Bush," but it's more in the sense of a dense and tough forest rather than a literal "mato" (grass).
Finally, the term "mato" in Brazilian Portuguese can refer to either grass or dense vegetation, depending on the context.
Have a great week!