Just looked at my contract with my Airline...I assume BA & all UK airlines have the same sort of thing in their contracts
"Must not make statements or write letters to the press concerning the compnay's confidential affiars"
So with this in mind, i assume the crew could either talk to the press or loose their Jobs...obviously it was in public interest for the CSD to be a representative of the crew in the press conference.
Hopefully...Aircrash investigation will make a programme on the events with interviews from the crew involved & witness accounts....