How to call her bluff
When Noone meets with Donna and reaches a point where he is not convinced that she is telling the truth about Peter, why not say to her, "Tell me now exactly where I can find Peter or I am using this telephone [points to phone] to call the Fuzz and you can explain it all to them!"
Simple.
But then I suppose we'd have no film. Plus, Noone was accused of, and recognised in himself, his tendency to embellish his own life for his radio audience. I mean, on the plane he told the woman next to him that Peter was his son!