In The Wicker Man (1973), Sgt. Howie flies to a secluded island inhabited by pagans to investigate a complaint about a missing girl, which was made via mail and includes the girl's picture. Why doesn't he seek out the person who filed the complaint and investigate its authenticity before pursuing it seriously? Is it just one of those cases where the plot expects the viewer to be less scrutinizing of the plausibility of the narrative?
Given that the note is anonymous, the best way to establish authenticity is to locate and speak to the mother, to confirm the child is actually missing.
If she says, 'Yes, it's true' - He's confirmed authenticity and can proceed by asking for further information.
If she says, 'No, it's not true' - He can mention the letter and question May Morrison about it - which he does, telling her that:
It's only that we have to follow up on information received [about a missing child]
The anonymous letter reads:
Dear Sergeant Howie,
None of us have seen May Morrison's daughter Rowan since last year. She's only 12 and has been missing... from her home for many months.She couldn't have left the island by herself. She's too young, and her mother won't say anything about it, just to mind my own business.
Well, I reckon it's all our business when a kid disappears, that's why i'm writing you this letter.
A child lover.
P.S. I enclose a picture of Rowan Morrison.
He tells the fisherman that:
I, as you can see, am a police officer. A complaint has been registered by a resident of this island about a missing child. Now, that makes it a police matter, private property or not.
He knows that May Morrison will be the best starting point, so goes to her sweet shop to find out more:
Following the conversation with May, Howie knows that something isn't right. The letter and it's author are perhaps now low priority, given that:
There may still be a missing child
There may be a conspiracy to cover it up
Both of which are probably more important to solve, than establishing who wrote the letter.