They made them small in case your mother-in-law comes for an extended visit. The majority of cape cods were built with an unfinished second story to save money for the homeowner who could finish it if he wanted. The floor joists do not extend the width of the house. They are positioned on bearing walls so the span is not as great as you think. The first floors were finished with larger joists because it was the main living area and contained the furniture with the most weight. Besides the contractor could save a few bucks by going with the minimum requirement.
Stand in the middle of the second floor rooms and bounce a few times. Does it feel solid, or are you ready to go for a dive. 6 inches is on the small side but if the actual span is within limits you should be fine. If you have any doubts you can contact a structural engineer and he will be glad to give you yay or nay.