No one just trusts. People spend years studying and using reason to come to faith. Read Mere Christianity by C.S. Lewis.
Believing in any truth statement is a mix of reason and faith.
Discussion
There are several prominent scientists and mathematicians that have come to faith from what they call overwhelming evidence in their field that both punch holes in the theory of evolutuon and point toward a creator.
C.S. Lewis is probably the most historic intellectual to do so and he wrote several books on the topic.
For comtemporary examples, I'd suggest these:
The founder of the Human Genome Project, Francis Collins, saw that as he dug deeper and deeper into the foundations of life that it only got more complicated and showed clear evidence of a designer. This lead him to conversion.
Steven Meyer is a Mathematician. He runs through the probablilities involved with evolution creating anything useful without decaying.
James Tour is a Chemist that has explored the extreme necessities of environment and resources to create foundational proteins needed for life, which cannot be created in cutting-edge laboratories, today.
They all have several youtube videos discussing their cases at length.
Frank Turek is a popular, modern Christian apologist that lectures and debates at universities. There are tons of videos of him, as well.
This is not a cut and dry, simple issue. If you think it is, you haven't given it the due diligence and intellectual honesty it deserves.
I understand that the existence of a creator does not necessitate that the Bible is reliable and true.
I think that most people aren't willing to entertain the latter until they have opened their mind to former through a review of the evidence on both sides of the argument.
Leading Bible Scholars are a surprisingly good mix of believers, agnostics, and atheists. There are a lot of good lectures about how they have come to trust the Bible's authenticity to the original documents, as it is a common argument that it has been changed with time. Other topics to look into are their evidence from Roman documents (not religious texts) on the death of Jesus and the 500+ witnesses to The Resurrection.
I’m under no obligation to do due diligence on every claim of supernatural events.
That's silly. Of course no one is obligated to do anything. Anyone can be as ignorant as they choose to be.
Due diligence in reviewing evidence is only required by those at the intersection of intellectually honesty and curiosity.
Most of my reply (above) is discussing the findings of scientists on the topic of science, not "supernatural events." Even if you come away with a better understanding of the weaknesses of the prominent theories, that is a move in the right direction, truth.
But, you are missing my whole point. My replies are giving evidence that the opposite of your claim is true. That religious people do make an attempt to verify, and that Christians encourage this over blind trust.
It also seems you are saying something different than your original post. Instead of "Don't trust, verify" being applied to everything, you believe: Don't trust, verify... except religious texts, you should just NOT trust those.
Here is a good example of secular faith. Leading modwrn atheist, Richard Dawkins, says he's baffled by The Big Bang. That it is contrary to common sense and modern physics is mysterious. That human intuition cannot be used to understand such physics.
He has to trust leading Physicists and take their word on how it works. Not even "trust me, bro" but "trust me because I trust them, bro."
The whole video is just ok, but the above can be found around 7:00 for suirces.