“Unbelievable” is hardly criteria for failure. In fact, it’s entirely immaterial, as long as the writer observes the only rule that matters about making sense: never pull the reader out of the vicarious experience.
Internal logic and consistency is important in helping readers stay in the vicarious experience.
I lean strongly toward the belief that readers want to believe, or at least suspend disbelief, and most will gloss over even glaring issues. I remember Michael Crichton’s translating earbuds in Timeline and after a moment of “Really?” I moved on and enjoyed the book immensely. (The movie, not so much.)
As writers we need to be as careful as we can, especially when the contrivance is core to the story’s spine and resolution. Coincidences and contrivances that make the story possible, on the other hand (like magic translating earbuds) are places where readers will go to great lengths to dive into a story they want to love.
It’s easy to go down the path my mom takes in stories, where she’ll spend 12 minutes talking to herself about whether Margaret’s middle name was Elisabeth with an ess or Elizabeth with a zee and in the end, accuracy had no bearing on the emotional impact of the story; in fact, the search for accuracy destroyed it.
I’ll take Crichton’s magic earbud over Melville’s endless treatise on whaling any day.
As writers, we tend to seek out readers who read like us. Your own experiences and dislikes are probably a good rule of thumb for what you can pull off with your own readers.