Formal proof in choosing between two competing assertions regarding fraudulent/honest claims?

Question

Please provide formal proof (or near enough, according to ability) for your decision as to which of the following two assertions is correct:

1. "Even if a claim is arrived at fraudulently, that does not mean the claim is untrue."

2. "A claim that is true, cannot be arrived at fraudulently."

A simple example of where the choice between these two assertions may come into play:

Someone publishes a claim that the Earth is flat. The claim is arrived at fraudulently, with empirical falsehoods and illogical reasoning. If we believe in the first assertion, we may consider the Earth to be flat, regardless. If we believe in the second assertion, the Earth cannot be flat.

EDIT:

To clarify, the idea of a "claim arrived at fraudulently" is that the claim is arrived at by empirical falsehoods, illogical reasoning is not enough, as any truth may be placed in an illogical sentence.

Answer 1

Suppose I say:

I was a member of Shackleton's expedition on the Endurance so I can tell you from firsthand experience that Harry McNish was the carpenter on that expedition.

The claim is that Harry McNish was the carpenter on the Endurance. This is factually true. However, my justification for this claim was fraudulent, because I was not a member of that expedition and have no firsthand experience of it.