I guess they're playing off the term of "birdbrain" (someone who is annoyingly shallow, stupid, and/or simple-minded; In this case, the lattermost association seems firmly applicable).
Kinda odd how lightly the first two avians were scolded, especially given that it was openly and immediately acknowledged that their behavior could potentially start a war.
Moreover, since Saints are nothing more than automatic cleaning devices, there's no inherent reason for the countries to not just tie them up and move them as they please. Presumably the reason the Saints can have the freedom they presently possess, is because of power balance reasons between the different countries, with the countries intentionally taking an off-hand approach to the Saints so as to avoid political complications. As the countries are segregated by race, instigating a war in this world could have disasterous consequences. Alienating the Saints, or giving the other countries a political justification to withhold them, would similarly be highly damaging.
In short, a mild scolding is.. surprising. Well, maybe the avians are so pathologically birdbrained that everyone is just used to their behavior by now.
Maybe it's kinda how we just shrug off corruption in politicians and police over in the States? Everyone's just far too used to it to take it seriously anymore..