Yes, but Augusta National gets to dictate terms, plus they've got right of refusal on sponsors. The contract for The Masters differs dramatically from anything else in sports, and because it is as big a tournament as it is (in terms of dollars generated, it is the biggest tourney every year, bar none), CBS (and USA for the early-week cable coverage) have very little wiggle-room.
There's no way that CBS/USA in their right mind would give the exposure up. It's akin to the NBA Finals or the Superbowl or the World Series. They'll make the money back elsewhere.
The key here is that Augusta National has held VERY tightly to tradition and contractually gets to dictate terms. If CBS/USA didn't like it, they could leave (!?). But once someone else grabbed it (and someone WOULD grab it very quickly), they'd acceed to the same terms, and they would get to hold it indefinitely, period.
Your question is answered in the article itself:
Rather than put its sponsors in a position where boycotts or their products or services would be threatened, Johnson said the Masters will absorb the advertising fees that would have been paid by IBM, Coca-Cola and Citigroup.
Actually, a lot of sporting events, especially golf, get on the air because the event officials, in this case the club or the PGA will pay the network to broadcast the event and then the club or the PGA will then sell their advertising time themselves. NASCAR did this before they made their deal with FOX and NBC. A lot of colleges do this expecially with radio. They will pay the station to carry their games and then sell the time themselves. Sometimes they will make a deal with the networks or the stations for them to also sell a certain amount of time also, or they will just keep it all for themselves.