How strange that there would be any debate at all. The point of the riddle is to obfuscate by adding irrelevant information. The ultimate question is "how many were going to St. Ives" to which there is only one answer deducible from the text. The answer your program gives defies "common sense" logic.
What are the arguments that the traveller should not be counted? Because the question seemingly restricts the set of things to be counted? That's just part of the obfuscation. I guess debate is what happens when "learned" people mess with a good riddle ;-)