Back-formation is just a process. If a language has a word that sounds like “prefix-X”, then back-formation is the process of creating the word “X” from it. Dis- is often a Latinate prefix meaning “apart”, “removal”, or “negation”, but in the case of dis-gruntled and dis-combobulate means “completely”, so the process of adding dis- and then removing dis- has changed the meaning of “gruntled”. It is therefore a new word (if it were the same word, it would have the same meaning).
Another problem is that the imported word may have changed in meaning. “Nonchalant” may have Latinate origin if you dig deep enough, but we really took it from the French nonchaloir to disregard and French indeed has the (uncommon) chaloir to regard. However, the English word “nonchalant” does not have the same meaning as the French word “chalant”—in English it is a feeling or attitude—so when you rip the non- prefix off you are not in any sense getting something that approximates the French “chaloir” that “nonchalant” was created from in the first place.
A final problem is that the affix may not exist in the first place. “Choate” is simply nonsense, “inchoate” comes from the Latin “incohare” which means to begin and there’s simply no affix to remove.
If you have a mathematical mind, think of it as non-commutative. You can add a affix, and you can remove an affix, and you can borrow the word into another language, but these are not commutative operations and the order in which you do things changes them.