Firstly, there are amino acids in grass, just not a lot, so herbivorous animals do consume aminos, and in the quantity of food they consume (litteraly hundreds of pounds for many species) they take in enough aminos for growth.
As for people growing on prison food, it is required that they are given nutritious meals, which include meat, and though it is usually of very low quality to keep costs down, it is still meat. Also, many of the guys that are getting rather large in prison are usually involved in some sort of work program where they do get paid and are allowed to keep the job as long as they behave themselves, and they use this money (I know it happens like this in some prisons, but not all even allow weight lifting) to buy things like beef jerkey, smoked mackerel (very popular), and even creatine with the wages they have earned. I would also not find it hard to believe that there are steroids in prisons, as just about any other drug can be smuggled in (there was an article in FLEX about prison bodybuilding sans the steroids part, which is my specualtion).
And no, aminos can not be made from carbohydrates, but they can be synthesized from other, more abundant, aminos (as long as EAA’s are present, which can’t be synthesized). This can not happen though, unles the elements that make up the functional group (which is specific to every amino, and what differentiates them) are available, which usually come from other aminos.