If you do not cross a picket line, that doesn't mean you let someone else go into the store for you.   If you boycott grapes to protest the treatment of migrant workers, you do not pick up a handful at the buffet table.

That is exactly what you do when you read a paper that you supposedly boycott.   When you read the paper, you are seeing the advertisements and getting the information that the editors wish you to see. Whether it is on your dime or someone else, the effect is the same.