This is known as a Dark Pattern; a user interface designed to trick people. From the DarkPatterns.org website:
A Dark Pattern is a type of user interface that appears to have been carefully crafted to trick users into doing things, such as buying insurance with their purchase or signing up for recurring bills.
In this particular case you are confirming a negative. The regular pattern for checkboxes is confirmation: "Yes (checkmark), I want to receive this newsletter". But in this case, you're confirming the opposite: "Yes (checkmark), I don't want to receive this newsletter".
If you were to say the second phrase to someone in regular conversation, they would likely have to pause for a short period of time to make sure they heard you correctly. They may even ask you for clarification: "Wait... you do want to, or don't want to?", because you just mixed a positive statement with a negative statement.
On the Dark Patterns website, these are called Trick Questions. Here is one particular example - Subaru Australia employs more checkbox trickery (February 2012):
The obvious modification, to address your question directly, is that the checkboxes should indicate the visitor wishes to continue to receive the newsletters. But it isn't that this company needs to be made aware their checkboxes are confusing, it is that they've made them that way on purpose.