'media training, trotted out in front of the cameras'
But that would presume that the people on the spot were in possession of all the facts to answer any and all questions posed, which is rarely the case, because it takes the relevant professionals (AAIB/NTSB) time to establish the facts and produce the accident/incident report.
So anything said too hastily is easily misinterpreted, and just as easily misquoted and utilised for other agendas.
It's also not an aviation thing. Any profession is best advised to take time in considering what it says, before saying it.
Determining what you know as fact, what you think you know, what may be determined based on professional knowledge and which is later open to revision upon new information, all takes time to avoid being misquoted.
Add to which, some people are simply not good public speakers, which can have a dramatically bad result. (Just look at GW Bush for tips on what not to do)
And now include the possibility that the person on the spot has just had a very bad afternoon.
Not a good idea, I think.