The mishna speaks about "keiva" which refers to the enzymes that line the stomach wall of the animal, and the "or ha'keiva" - skin of the keiva, which is the actual piece of the stomach wall. The keiva is considered merely "pirsha" and therefore concludes that even the enzymes that line the stomach of a neveila or treifa animal can be used, but one cannot use as rennet the actual wall of the stomach of a neveila animal.
Rashi discusses milk that is found in the keiva of the animal that is then salted together with the stomach of the animal. Rashi points out that to permit using this milk that was salted with the stomach as rennet, we would have to assume that the milk found in the stomach qualifies as "pirsha" similar to the enzymes. Rashi rejects this notion and considers the milk to be actual milk so that when salted with the meat of the stomach qualifies as meat salted with milk and becomes assur m'drabonon as bassar b'cholov. We would then say that חתיכה נעשה נבילה so that all that milk has status of issur and when used as rennet will spread issur to all the milk since we say min b'mino is not batul (this is rashi's opinion 109a and many other places that we pasken min b'mino isn't batul. tosafos disagrees and holds that we pasken min b'mino is batul - but in this case where it is effective in being ma'amid the cheese, even tosafos would agree that we don't say bitul).
Rashi implies that had we considered the milk inside the stomach to be merely "pirsha", we would be able to compare this case to fish that was placed in a meat dish, which can be eaten with milk using the concept of נ"ט בר נ"ט, meaning a second generational no'sein ta'am. Both the Rashash on Rashi and the Shach (y.d. 87, 31) point out that even if we were to consider the milk that was salted with the stomach lining to be "pirsha" it would still not be comparable to the hot fish on a meat plate that can be eaten with a dairy food. The concept of נ"ט בר נ"ט only applies when the second generation flavor stand alone as a permitted entity that you are now going to use with milk. However, when the milk is salted with the skin of the stomach, the "pareve" milk inside the stomach absorbs a ta'am rishon of meat. We then take that ta'am rishon and mix it with milk to create cheese. Since the ta'am sheini of meat is immediately mixing with milk, we consider that to be an issur. Rashi writes that he originally thought that the milk in the stomach qualified as pirsha and was matir, implying that he holds that if the milk were truly pareve because it was considered to be "pirsha" then we could compare it to the case of hot fish in a fleishig plate that could be eaten with milk, and doesn't seem concerned with the aforementioned distinction.
Rashi 111b (d.h. nosein ta'am) writes explicitly that one cannot put hot milk in a fleishig bowl because the second generation flavor of meat is going directly and immediately into the milk. The case here, even if we consider the milk in the stomach to be "pirsha" should be exactly identical to the milk being put in a fleishig plate where Rashi himself holds that it becomes assur!