Final answer:
The provided textual references do not contain information about Peter Wilks's English brother, making it difficult to determine the authenticity of the king in the specific context of the question.
Step-by-step explanation:
The first thing that cast doubt on the authenticity of the king being Peter Wilks's English brother in the provided context doesn't appear to pertain to any single event or anecdote that directly correlates with the question. Instead, the textual references provided seem to discuss historical events surrounding English apprehensions about Catholic monarchy, the behavior and misfortune of a character named Duncan, a narrative about a werewolf, James III and the throne of England, and a character named Eckert who was known for lying. However, without a direct reference to Peter Wilks's English brother from a specific text, precise determination remains challenging. It's possible that the question refers to an incident in Mark Twain's 'The Adventures of Huckleberry Finn', but the provided excerpts do not include such an event.