2 answers
The way SF works in general, is they allow you much more flexibility for selectively opening up access to records, but not so much flexbility with selectively limiting records. In other words, generally you need to lock things down to the level of your least accesible scenario, so in your case, someone who shouldn;t see the campaign, and then open it up to others with sharing rules, manual sharing, etc.
It might be a pain but you may need to change your sharing settings on Campaigns to private. then you can use Sharing rules or manually share the campaigns as you need to allow users to view them.
