Yeah, he's right. The only network that is forced to air everything scheduled is ABC. All of their affiliates have a contract stating that they cannot air over or reschedule anything on the schedule.
Maybe that particular station isn't given any outs, but that's not the case for every station. It all depends on how much they can/want to negotiate with the network. Many, many years ago I worked at a station that specifically had it in the contract that they didn't have to carry weekend editions of the CBS Evening News. In carving out this allowance, it didn't hurt that our general manager was the president of the CBS Affiliates Board.
Also, as I've mentioned many times, FCC rules specifically say that a broadcast station can not be
forced to air any show, ever. The worst that can happen to a station that violates a programming contract is that they lose any compensation they have coming to them and the contract is cancelled. (And they theoretically might have to pay a penalty if one is written into the contract.)
The network doesn't "force" them to carry anything. There are several affiliates that have dropped CBS's morning news shows over the years.
CBS first started The Early Show at a time when a whole raft of stations were threatening to drop The CBS Morning News. To keep them, they actually reformatted their clock in a way that allowed stations to fill about 75% of the first hour with local programming if they wished. CBS only dropped that "flex" schedule a couple of years ago.