The perception may come from old writings for medical tinctures and the like including the instruction to “say three Hail Marys”. This wasnt a magic incantation; it was a way to measure time for people who did not have watches.
A few years ago I heard about some folks who found a very ancient recipe to cure MRSA. The strain evolved away from being affected by that recipe in the past and it was abandoned, but this much later that recipe worked on modern strains. Included were the instructions to say five(?) Hail Marys, which translated to “wait five minutes”.