Again, that varies from community to community. There are some communities where there is less religious fervor, and more just following tradition, and there are other communities that see their religious experience as the most important part of their identity. The stories you are referencing tend to come more from the communities that emphasize tradition over religious experience.

Many people make the mistake of thinking of Amish as a single uniform blob, whereas in fact there are many very distinct subgroupings that don't have much to do with each other. In the state where I live, for example, there are at least 3 different distinct Amish groups (each with multiple communities, expanding at a very rapid rate), each of which does not necessarily consider the others to be true Amish, with the dividing lines primarily being this difference on or not tradition is prioritized over religious experience.