What are you people talking about?
We went to Tijuana and when we came back, those very mean Mexican American custom police asked for passport, green card, or visa. A friend of mine just carried his Calif driver's license with him, they gave him 3 options: paid $300 fine (for some document searching, validating, etc. that we didn't know), stayed in Tijuana until his family send him his passport, and lived there in Mexico.
Conclusion, bring the passport with you, your student ID, driver license, etc. do not count.