Ok, just to be clear that's your (and my own) opinion, not necessarily a legal fact. If you have info that says otherwise, then post it.
Here's the only other article I could find.
http://www.latimes.com/news/printedition/california/la-me-almazan15oct15,1,5004090.story?coll=la-headlines-pe-california
See #28. Illegals cannot enlist.