My builder/AC Contractor claimed that my duct system(s) do not leak, why should I not believe them?
Trust, but verify. If they are so sure that there is no leakage, there should be no problem in verifying the claim. It is a relatively cheap insurance policy that the duct system is smoke tested to be leak-free. In any event, the claim should be questioned, since leakage is invisible even to the best of inspectors.