Negative publicity or affiliates may end up eating a large amount of the search results for your brand name.
If it is negative publicity of course you should take the message on board, but what do you do if you solved the problem and the bad search results will not go away? Directly contacting them and showing the problem has been fixed might help. Maybe even offering to donate to a charity may help, but if the person will not work with you it is going to be up to you to create other content that can be deemed more authoritative than theirs.
If the affiliates add a lot of value of course them listing below you for your brand name is no big deal, but what happens if they are thin affiliate pages that add no value, or worse yet try to use your brand to push people to a competing product with a higher payout? Is there another way to add search results to the index that will not cost you a percent of your sales?