Dave:
Should we believe Mark Carney?
Well his stance immediately prior to the Brexit vote is available in The Guardian and it is possible that, even now, he does not want to admit he was wrong.
Other views question his latest comments, as in The Spectator

So it's not a case of deciding who is more likely to be believed, me or an ex-governor of the BofE.
The above Guardian quote (of Carney) even shows that he was only claiming half the pre-vote fall in the pound was due to risks associated with a vote to leave:
The Bank noted the pound had already depreciated 9% since a November peak and that half of that was down to the “risks associated with a vote to leave the European Union”

The situation is a lot more nuanced than it at first appears.