i believe both Hertz and Budget (Avis) operate as independent franchises in Mexico. They are run by an independent business owner, and not by the US companies. Thus, the rental experience might be different than what you are accustomed to in the US.

you could always try calling the local Hertz reservation # in Mexico and tell them that you have a lower quoted rate with Budget. Since they are independent, they might have more leeway with giving you a better deal