Checking the race box is not enough. If you wanted adcoms to consider your race, you should have made it clear. Checking the race box does not do it. You have to talk about how coming from a different culture makes you different from the other applicants who have the same LSAT scores and GPA that you do.
Hmm..I'm not so sure this is true. While I think a lot of people would like there to be some requirement for you to be "into" your ethnicity to receive the benefits of AA, I don't think it's requisite. And I don't think it should be. You might have gotten more "Mexican points" if you were more involved with ethnicity issues, but I'm sure your ethnicity counts even if that's not the case (and I'm not sure your "involvement" makes any difference at all to adcomms, honestly.)
Don't think it really matters if the diversity statement is well written and says what it needs to say about your background. Good luck.