I think that the rule is reasonable as it refers to a 'statement from the council', not the opinion of a councillor, officer or any member of the staff. If the media ask for a statement from the council (oral or written) then it should go through the clerk and be handled in the manner laid out in council procedures.
However, if the press ask for an oral statement or written one from a councillor (who cannot be the council, unless delegated to represent it by council procedures along with all the rigmarole required) then that is not covered by this rule. The councillor would have to make sure the recipient knew they did not represent the council. I would expect the staff would be in the same position, and if the clerk were asked to give as statement they could not do so, as it would compromise the proper officer position.
I think a lot of the rules are written without much thought as to how they work in practice (as the rule above talks about staff, and the proper officer is a member of staff), other than to gag councillors, as noted in other answers, but there are sufficient holes in them to allow councillors to speak to whoever they wish to, as long as they make sure people know its not a 'council' reply.
That other councillors interpret the requirement in different ways supports the view that it was written without much thought as to how it is operated in practice. Recently a council passed a motion for all councillors to read and sign that they understood certain documents. As a then councillor I asked that this be done as a council, as each councillor could read the documents and come to different conclusion as to how the various requirements processes worked. A lot of councillors were not happy as that takes time!