Meeting held under this rule do not allow the the disclosure of who said what. The "what" can be reported, but no-one is permitted to say who said it. That permits people to express views, or ask "what if" questions (and get considered, informed answers) without having to always play to the (media) audience and make guarded, ambiguous and watered-down statements.
Since the government recognises the value of these sorts of meetings (as well as the established protocol of "off the record" briefings, which cannot be quoted) it's ludicrous that they would think that removing anonymity would be a good idea. This can only be one of those "silly season" media reports, usually made up by journalists who are bored as politicians are away during the summer months.