Nom, cholim are definitely allowed to eat before davening.
But there’s a huge difference between shacharis and mincha/maariv. The former is a pasuk and understood that it’s gaavah(this is why drinking water and tea, coffee, is allowed, because it’s not gaavah)
Before the latter, it’s simply because one might forget to daven
So if they have a set time, like in Yeshiva, it’s mutar; same if you have a shomer, etc..