This company history said the line was changed "In response to requests from the Rockefeller family," but other sources claim the Rockefellers sued.
This Google Search will lead you to a number of sources, none of which appears to be authoritative. My guess is that the coffee company would have been "Nuts" to deny a Rockefeller request, and there would have been no need for a lawsuit.

The company Website is http://www.chockfullonuts.com/ - you can hear the current version of the jingle there.

-Joe-