Healing shrines

Here's an interesting installment in their ongoing series:

https://billdembski.com/theology-and-religion/faces-of-miracles-chapter-8/#more-54827

However, I disagree with how the issue is framed:

So how can anyone, even if favorably disposed toward miracles and healing shrines, know for sure that a dramatic improvement or cure was thanks to a pilgrimage to a healing site and not due to natural healing, psychological factors, or some unexpected change that could still be explained in naturalistic terms?

1. That's a false dichotomy. As I've discussed before, I think the real question is the basis of comparison. Given the nearly negligible number of confirmed healings at Lourdes in relation to the total number of pilgrims, why assume they were healed because they went to Lourdes? I mean, don't you have to compare it to the percentage of miraculously healed people who never went to Lourdes. Are the odds higher of miraculous healing if you go to Lourdes? Is there any statistically measurable difference? Once again, given the exceedingly low correlation between confirmed healings at Lourdes in relation to the total number of pilgrims, would they experience miraculous healing whether or not they went to Lourdes? 

Suppose a hundred cars have flat tires within the same half-mile stretch of freeway. Is that suspicious? Does this mean that for some reason cars are more likely to have flat tires at that location? Is someone scattering tire spikes along that stretch of freeway? 

But doesn't that inference depend on the basis of comparison? How many cars have driven along that stretch of the freeway compared to other sections of the freeway? Over how many years have a hundred cars gotten flat tires along that stretch of the freeway. And how does that compare to flat tires along other stretches of the freeway, over the same timeframe? 

2. I'd add that if Roman Catholicism is true, and God made Lourdes a healing shrine to validate Roman Catholicism, it's passing strange that he left the evidence so ambiguous by making the cure rate so vanishingly small.