The thing that bothers me about the idea that the average adult "should" know various things about how sports are played and who the teams are and whatever else has been brought up in this thread is that, despite other examples of culture (popular or otherwise), the "should" thing doesn't come up for other things in nearly the same way it does for sports.
On the contrary, I would identify knowing what Lincoln Center or the Met to be as important as knowing the name of sports teams. Or knowing if your city has a symphony or opera or ballet company in residence. Knowing the difference between stringed, brass, woodwind and percussion instruments. Recognizing the names Bach, Beethoven, Mozart, Picasso, Monet, Rodin. Knowing what museums are available in your vicinity.
For example: my family are avid attenders of museums. We will go to a museum about anything, on the assumption that if someone thought this stuff was worth collecting, it's worth going to see. One year, my sister's in-laws took her children to another city on vacation, and when the kids came back, my mother was asking about the trip. Did they go to Historic Site A? No. What about B? No. C? D? E? (these are all sites where our parents took us when we visited). No. Finally, my mother asked, where DID you go? My nephew replied, 'We went to WalMart.'
This, in a nutshell, is the difference between the two families.