Neonatal pups do not yet have well developed immune systems. They are born with some maternally dervived antibodies in their systems which provide a small degree of protection durng this period of immunological vulnerability. But most young animals get immunological protection from antibodies found in the mothers milk, specifically in the colostrum. In neonatal animals with poorly developed immune systems, proteins as large as antibodies can pass through the lining of the gut, and can provide functional protection. As the young animal matures, their own immune system develops and can provide protection. At the same time, the gut also matures and proteins such as antibodies can no longer pass through the lining and are digested with all the other proteins.
Bacteria are everywhere, no matter how careful you are. Most of the time they don't cause any problems because our immune systems can keep them in check. My best guess as to what is happening in your bottle-fed pups is that the maternal antibodies they are born with are no longer providing functional protection, and they are not receiving additional protection from colostral antibodies, so they are not able to keep the bacterial population in check until their own immune systems are developed enough to take over. This is just a guess - I don't know in dogs or wolves what the time line is for pups to develope functional immunity.