The river is famous to the fish. (1)
Why is the river famous to the fish? Why isn't the river famous for all the wonderful things it does and is? Celebrities are famous for their work on a particular film or for the complete disaster that is their personal life. Why does Nye emphasize whom people and objects are famous to?
The cat sleeping on the fence is famous to the birds watching him from the birdhouse. (5-6)
The birds only care about this particular cat because he is too close for comfort. Sometimes in community, the 'other' or 'the outsider' is only viewed as a danger because of how close he is. You'd think a whole lot differently about that odd fellow on the other side of town if he suddenly lived in the apartment above you.
The tear is famous, briefly, to the cheek. (7)
Why isn't the tear famous to the eyes? Is the tear famous to the cheek only because it is imposing itself on the cheek? This tear, though, leaves no lasting impression. As quickly as it's made famous, it's forgotten. Perhaps Nye is telling us that momentarily blipping on the screen of someone's life (or even starring in a multi-Oscar-winning film) isn't enough to make you famous in the long run. You have to make a lasting impression. (Maybe a couple of multi-Oscar-winning films would do it.)