It doesn’t bother me when people believe these stories. Presumably some happened and some didn’t. Whether or not they actually happened is irrelevant as hopefully the message gets through. (And yes, when the only message of a story is “look at how great this Rabbi is/was” then I tend to ignore it; I don’t need apocryphal stories to tell me the greatness of Gedolim-their Torah does that.)
What does bother me is when people think that someone who doesn’t believe these stories has a P’gam in their Emunah.
It also bothers me that someone who would say the Rambam’s definition of Hashgacha Pratis would probably be shouted down as an Apikores nowadays.