If enough people go to Lourdes and claim to be healed but upon closer inspection those numbers are less than what you would expect from just the placebo effect, or they weren't actually sick in the first place, or were not in fact cured of actual illness, etc. than it is very good evidence that there are no miracles happening and that the people who think they are are unfounded in there beliefs.  There is no bias in that.  I would agree that it doesn't rule out the possibility that there is a god who doesn't take a hands on interest in human suffering but why care about that.