They are entitled. Possession by right of conquest is recognized by the Law of Nations.
Spain abandoned the territories at issue, in some cases under the application of force by Mexico. Mexico, therefore, occupied some of the territory abandoned by Spain but claimed it all. However, Mexico was unable to maintain control over all it had claimed. Hence, some of the territory at issue was seized and held by Mexico by right of conquest, and some remained beyond Mexico's effective control. This latter, then, became unclaimed territory despite Mexico's assertion otherwise (a claim that connot be enforced has no standing).
When we (the US) won the war with Mexico, we settled the boundry dispute Texas had with Mexico, we claimed the territory abandonded by Spain, and took the balance of the disputed territories from Mexico by right of conquest (Texas, an independent nation for ten years, applied for admittance into the US and was accepted).
We hold these territories by right of conquest. Aztlan can claim these territories by right of conquest. At some point, one of three things will happen.
The federal govt is at present on the path to surrender in the SW, but it may not happen very smoothly. There are millions of hardcore gringo cowboys in the SW who will not meekly pack up and leave. It will be a bloodbath, it will be Bosnia X 100.