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I offer flat monthly fee advertising, which works out better in many cases. Also the advertiser might want actual text links that can be indexed. And it's nice to build a relationship that can last a long time. Many of the flat monthly fee advertisers we have have been with us for almost 2 years.
Another advantage for the advertiser would let us (site owners) to introduce him to other related websites they may be interested in advertising on.
But I am not going to do this if it breaks the TOS
It's possible that the deals you could strike with the other website could pay you more than Google does, but obviously you'd have to no longer participate in adsense if you wanted to contact direct them direct. However, if they contacted you first that's another matter.
Very strangely, a great many people have had trouble reading this part of the T&C and have drawn the completely erroneous conclusion that it forbids contacting advertisers for any reason. In fact, the language is extremely precise that the only subject you are forbidden to broach with advertisers is the subject of any Google ads or Google links displayed in connection with your websites.
But simply contact Google if you are uncertain.