In my story, try proving with evidence to the man eating a hot dog in a Chinese restaurant that he committed the crime
Your analogy glosses over the real world situation.
If the man was really eating a hotdog in the restaurant, there will be evidence of that.
His DNA and fingerprints in the restaurant, people who saw him there, security camera's, hotdog in his stomach, etc. etc.
In that case there's reaonable doubt that he is the perpetrator.
Of course, if he just claims he was in the restaurant, but there's no evidence to prove it, and much compelling evidence to the contrary, why believe him? He may be lying or be (very) confused.
Similary, if people just claim something based on their specific interpretation of a religious book, why believe them if they present no evidence to backup their claims, and there's much evidence to the contrary?
Without evidence, these claims are useless. At best, they are just opinions. At worst, they are factual incorrect as shown by available evidence.