Story behind “On the Internet, nobody knows you’re a dog” cartoon

In an interview with New Yorker magazine cartoonist Peter Steiner, CartoonBank blog (dead link; I picked this content from their feed) asked him: 

Your cartoon, “On the Internet, nobody knows you’re a dog,” is one of the best-selling New Yorker cartoons of all time – and, since it was published in the early days of the Internet (1993), it is considered a prescient sign of changing times. Can you tell us the back story of this cartoon? At the time, did you have any idea how significant it would become, or did the image of two dogs logging on just strike you as funny?

He answered: I didn’t even think it was that good. I put the two dogs there and then I put the caption, and it became this huge phenomenon.

So there is no story after all, behind this famous illustration in Internet history 

Peter Steiner is also a novelist & a former professor.

Related: A recruiter contacts a dog for a Java/Python developer position