Barthy said that? I remember him saying that Sanctum fal'Cie couldn't destroy Sanctum because of their nature, which would lead one to believe they can't give their l'Cie a Focus of destroying Sanctum and by consequence Sanctum fal'Cie. However, I don't recall him every saying that about Pulse fal'Cie and their l'Cie.

(SPOILER)
From what I understand Sanctum fal'Cie cannot destroy Sanctum. It is simply against their nature. While they might want to destroy it, their nature is to preserve Sanctum. It would follow that their l'Cie cannot be given a Focus that would contradict their nature or if they did they would be insta-Cie'th. This is shown in Chapter 13 where most of the Calvary is turned into Cie'th We do not know much about Sanctum l'Cie because the only living one is Dahj and his Focus was to protect the Sanctum fal'Cie by tracking the Pulse l'Cie. This reinforces the very fact that they cannot destroy Sanctum.

Now Sanctum itself is composed of a bunch of fal'Cie who are arranged into a hierarchy with Eden on top. All these fal'Cie work in concert to sustain and protect Sanctum. So a threat to one is to threaten Sanctum which means you are attacking them all.

On the other hand, we have Pulse fal'Cie whose goal is natural landscaping, more or less. Each Pulse fal'Cie has his own area of governance (Atmos is underground digging, Bismark is water, etc...). Whereas the Sanctum fal'Cie work in harmony to sustain Sanctum, the Pulse fal'Cie do not have such a hierarchy and work independently from one another. Like their Sanctum counterparts, they are protective of their sphere of influence (such as Bismark's reaction to your presence) but they do not have the same interdependent relationship.

Due to the independent nature of Pulse fal'Cie, it is possible that their l'Cie could kill another fal'Cie. Whereas a Sanctum l'Cie attacking another Sanctum fal'Cie would be a threat to all of Sanctum, the same is not true for Pulse fal'Cie. I would also argue that a l'Cie could not kill their own fal'Cie. Anima was not destroyed by your party. Perhaps weakened by it still had enough power to turn the lot of you into l'Cie before it crashed down and made pretty crystals!