"he wasn't expressing opinion he was stating a fact".
That's your opinion.
It is still true that the CDS made himself available on BBC to answer a specific question about Corbyn's previously expressed refusal ever to use the nuclear option.
I don't see it as the CDS's job to do this in a public forum. Nor would it be within his job description to express public support for the deterrent in the event that Marr ever invites him to comment on the current government's nuclear strategy.
His job is to do what he is told, quietly and behind the scenes. He can offer his views through the appropriate channels but these do not include public statements on the BBC. If he doesn't like what he is told to do and cannot persuade his political masters otherwise then he should resign.