The designer Hans Hulsbosch says''Based on this logic, they would have to take action against every fruit-seller.''

This isn't the first time Apple has accused a company of ripping off their logo. Just last year they accused Victoria School of Business and Technology for copying their logo, also an apple. Back then they said

"Your business logo…reproduces, without authority, our client's Apple design logo which it widely uses. By doing so, you are infringing Apple's rights, and further, falsely suggesting that Apple has authorized your activities."Apple declined to comment on the issue with Woolworths.
I think Apple is going too far in protecting their brand. I wouldn't even associate the company Apple with Woolworth's logo. I like how they incorporated a W in their logo and thought that was clever.
It's also a little hypocritical considering the Beatles' record label, Apple Corps, sued Apple three years ago for stealing their apple concept and logo. However, Apple won that court case (link) so I guess they feel that it's "theirs".
So to all designers out there, apples are off limits.
~Christine