I'm a little confused by the question. Are you asking the question in your first paragraph, or how to respond to a claim about that?
Anyway, most undergrad math classes in the US with a final exam I know about have the exam as one component of the course grade, as in Nate's comment. The grading policies should be written clearly in syllabi and occasionally there are clauses like the final exam grade is a lower bound on the course grade, but I have not often seen the other way around.
If you want to respond with data, you would need some sort of survey, but you also need to clarify meanings as there need not be an inherent meaning of "passing a final exam." The instructor may set a cut-off and call exams over certain scores passing (though this is sort of artificial if the instructor "curves"), but I never assign passing or failing grades specifically for the final exam, so for me "passing the final exam" means doing well enough on the final exam to make one's cumulative average high enough for me to assign a passing grade.