It's pretty much a trope of entertainment media that when in some kind of plot hole the writers can't dig them self out of, statistics is the go-to relief-force to find the criminal, solve the puzzle or convince the stragglers. I would say something like "common people" think of statistics as being some sort of magical force that binds the universe, but pretty much everyone from all over the IQ (and autism) spectrum nowadays place a cult-like reverence in the numerology that is statistics.
Statistics is the use of numbers, so that already gives the aura of potent abstraction to any claim, study or aside that's statistically justified. People are natural Platonists. They like to think that the real world is a shadow of a more elegant numerical reality. When people hear statistics, they assume that statistics are some higher order of truth than the world around them. That's backwards. There may be numerical truth to the universe in physics, but statistics is messy numbercraft where we take data from messy realty, brush off the dust and try to approximate underlying truth.
Most of the time, using statistics has the same sociological use as using big words. When you're bored, afraid of being proven wrong or running out of stuff to say, statistics is that lifeline to make you look smart and reliable.
You can always tell when you read a study written by someone unsure of their work. Statistics will be overused, misused or simpled avalanched onto the paper to dizzy the reader into a tactical mental surrender.
It's sort of reminiscient of postmodernesque writing, where the author tries to cloak something childish or uninteresting in fancy garb to make them a little immune from critics who don't want to waste the cognitive energy of disrobing their inanities. At the very least, it looks smart to the uninitiated.
On this side of academia, this is a technique often consciously cultivated by people in the field. When a colleague or grad student has come up dry in a study, a common piece of advice is to simply running more statistical tests. Linear regressions, t-tests or at least p hack better! Getting this type of advice is actually a good sign you should cut your losses and move on.
An even bigger problem is that this kind of manipulation can become unconsious. Statistics seem like the keys to the universe. The reality is that it's just a grab-bag of algorithms we've invented that can be used to haphazardly approximate unknowns. It's my firm belief that back in the day when a lot of statistics was done by hand.people doing the math had to stare at the paper thinking "I am applying a series of algorithms to approximate unnknown data and analyze the data I have. This isn't magic. It's a desperate stab in the darkness." Nowadays, you plug input into a computer and it spits out whatever was programed into it. The same formal operation, but in the second case, it seems like magic.
When people are divorced from the math and assumptions of statistics, or aren't well-informed enough about it, they place inordinate faith in it. People naturally deify what they think is inconprehensible. Because of this, statistics often seem more comfortable even when qualitative analysis would be much more informative. Because of that, people will often do statistics to export their epistemological concerns about their own projects into some mystical void. If you were doing it by hand it wouldn't happen, but big-data statistics has become a black box that takes in your uncertainty and poops out something that looks really smart.
I've seen articles talking about how statistics will solve all of our epistemological problems. How we won't even need "theory" even more now that we have "data," AKA "truth." The esoteric truth to statements like these is just that statistics is a tool for forgetting our concerns and for providing a mechanistic certainty we wouldn't ever otherwise have..