Does an online paper need a print presence?

Since the Seattle Post-Intelligencer closed Neilson reports traffic to the online-only paper has plummeted. The Seattle P-I folks say it's not true. http://www.washingtonpost.com/wp-dyn/content/article/2009/04/22/AR2009042202654.html

Time will tell, but it does raise the question of whether a online edition needs a physical presence somewhere? Does Time Magazine keep its reputation if there isn't an actual magazine somewhere? How important is that incidental contact that print newspapers and magazine derive from being on the racks, in the honor boxes and lying around in waiting rooms? Can you sustain visibility over the long haul without it?