Is objectivity not being based on facts? And facts are those things people have consensus over. If someone does not believe the facts, claiming objectivity is just am attempt to elevate ones-self above needing to explain your reasons to believe certain things.
Even when someone claims to be objective and is using facts that consensus is agreed on, the wording may well not be objective. Or that person could just omit facts.(by accident or purpose)

I think news organizations usually erroneously claim objectivity. Although this has had its use when they need to report on something as bystanders, and not be dragged into the events. (But it usually does not work.)

Or am i approaching this thread at a wholly different angle? Perhaps you are talking about the "The price payed" thread? Is that not talking about feelings associated with a picture? Perhaps that is a kind of lack of objectivity too.