Once we had the kind of Group Officer who, if he showed up at 2am to a fixed alarm, we would welcome with open arms. Unfortunately he's gone the way of many of our really good people and left the service.
I guess the GO's span of control is the whole group and if they choose to come and have a look see at an incident it is completely withing their "operational (and other) responsibilities".
And if the OIC of the single Brigade involved believes that the GO is taking over control unecessarily I guess they can advise the GO of that
And if the GO wants to take over anyway, maybe they don't trust the Brigade OIC.
And if the Brigade OIC's think the GO is an annoyance and a siren jockey I guess they don't vote him/her in next time round.