The logbook does not record the legal owner, just the registered keeper. If he is the owner, he can do what he likes with the vehicle. If he doesn't own the vehicle, obviously he can't part exchange it without the owner's permission.
In order to notify DVLA of the disposal, the registered keeper has to sign the logbook, so I presume if you are not prepared to sign it, he is going to forge your signature on it. That is obviously not allowed.