More humility and less arrogance would have stood them in good stead from the outset. The classic being the English social worker who went to assist immediately but was told in no uncertain terms to go away.
At a time of distress, how she was welcomed might have depended on how she handled the situation.
If she came across as bossy-boots (and clearly didn't have a legal mandate), she could have been from a tabloid, for all that anyone knew in that immediate aftermath while the press were gathering.
On the other hand, her desire to help may have been quite genuine. However, if she wanted to talk to a hysterical Kate on her own to question her about the disappearance as a potential parental abduction (in the event one or the other or both weren't the biological parents), all three knew that this wasn't the case and her appearance could no doubt have appeared ill-timed.
I could have accepted that until her supposed suspicion about the third person present. Why on earth didn't she do a bit of basic research prior to communicating that name to the police with her suspicions?