Well I'm from Mexico so my answer is a resounding YES, everything here has hot sauce, foreigners complain that when they ask for "no sauce or peppers" with their food, they still give them peppers with their food hahaha, the question here is not wheter you want your food with sauce or no sauce, but rather a lot of sauce or not much sauce.
I've heard a lot of theories as to why Mexico's gastronomy is entirely based on chili, the most amazing and credible is that back in the Aztech days, they used to have famine and food wasn't that abundant, so they had to eat, lets call it "old" or "rotten" food, so they added chili to the food to mask the rotten flavour. There is stew called 'Pozole' its really popular, it has chickpea, meat, letuce, etc.. and a lot of chili, it is delicious, however the legend behind it is quite dark (and don't know if its true), it is said that when the Aztechs made human sacrifices they chopped up the body parts and made this stew called Pozole for everyone to eat, fortunately we no longer do that hahaha It is said that when the spaniards arrived to Tenochtitlan, which was the Aztech city with the piramids, the piramids were covered with blood, which was a product of human sacrifice. I believe the Aztechs were perhaps one the most barbaric culture in history.
It is a problem, whenever I get a stomach disease, its is so hard to eat anything because EVERYTHING is spicy, with sauce, chilli, etc...
The rule here is if some Mexican tells you something is not spicy, it is definitely spicy. Avoid red, yellow or orange sauce, or peppers, green sauce tends to be lighter, but still some of them are rabidly strong. Even american fast food restaurants have a lot of chili hahaha, there are mexicanized breakfasts from McDonalds, Burger King, KFC, even Pizza, the mexican pizza is full of chilli peppers and we still add hot sauce to it.
A basic food here in Mexico to give to the poor is hot chilli pepper, it is a fundamental part of our diet, we use it in everything. You can buy in the supermarket these donation cards to give peper chilli to the poor, or beans, or rice, and tortilla of course.
Ohh and the 'Mexican' food you have in the US is not Mexican at all, it is TexMex, I do like it thou... When I lived in Ohio around 5 years ago, I did find a couple of real mexican restaurants, one of them was specially good, and its really funny how happy the owners get when they find out you are mexican, they sit with you to eat, they chat, they ask questions, they treat you like an old family member even if you are complete strangers etc.. etc.. I love that about the US, its a very diverse country, everyone feels American but they still feel so proud of their origins.
Fun fact, a tribe of the Aztechs were called the Mexica and they founded their holy city based on a legend about their God Huitzilopochtli, who told them to settle and build their city at the place where they found a snake standing on top of a cactus devouring a snake (that is the coat of arms in the middle of the mexican flag) , which is why the country is called Mexico as in "the place of the Mexica", and what does it mean in the native language? it means "The moon's bellybutton". Well, that doesn't have anything to do with hot sauce, but I guess Now you know ;D
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