If the deadhead is required by the company then it is not rest. It does not count as flight time.
Which is true regardless of whether the deadhead is in the actual jumpseat, in the back, or riding in a van (as long as that transportation is not "local in nature").
I too am curious as to what crusty the captain thinks has changed. It's possible that in the brave new world of maximizing efficiency that the captain is starting to run into FARs they've never had to deal with in the past since they were protected by union or company rules.