One limitation of the analysis is that it relies on data gathered far down the line from the actual criminal behavior. Between the act and incarceration rates are many steps: reporting the crime, arresting, prosecuting, convicting, and sentencing the defendant as well as deciding when he gets paroled from prison.
The data closest to the act is self-report data. The National Longitudinal Study of Adolescent Health (Add Health) is a longitudinal study of a nationally representative sample of adolescents in grades 7-12. In the study, 3,911 whites and 719 Hispanics answered if they had committed the crimes listed in the table below. Percentages are displayed as well as the ratio of the Hispanic to white rates.
Of the 15 delinquent acts listed, Hispanics have the higher rate 14 times. Ratios range from 0.95 to 2.33.
Critics might respond that surveying adolescents captures minor crimes, while data on prisoners, for example, captures serious criminality. But you can see that respondents were asked about very serious crimes as well as about less serious ones. For example, Hispanics are 2.33 times more likely than whites to have stabbed or shot someone (and the difference is statistically significant).