Correct. My (mostly rhetorical) question is why is Facebook installed in this way? It certainly doesn't need to be. It runs just fine on phone/roms that don't preload it, installed as a user app.
My phone is rooted, and I've uninstalled it properly using Titanium Backup. There were also hidden Facebook "app installer" and "app manager" apps, which I removed.
My understanding is that "system app" just means it's baked into the ROM. So it's not actually possible to uninstall it without flashing. Disabling removes it from all the application lists except the one in settings where you can re-enable it. [0] My guess is that the rooted uninstall is removing it from all system lists. But the binary is still there in your ROM, unless you've flashed a new ROM that removes it.
[0] This is also why the disable button dialog discusses uninstalling the updates to an application. Because updates are obviously not written into the ROM; they're in normal application storage.
ROM might imply that it's a different hardware storage device or some such. That's not normally the case; it's just a different partition mounted at /system. User apps are in /data/app while system apps are in /system/app.
/system shouldn't normally be writable at runtime on non-rooted devices, so updates get installed to /data/app like user apps. A proper uninstall with root, e.g. using Titanium Backup does remove the app from /system/app.
My phone is rooted, and I've uninstalled it properly using Titanium Backup. There were also hidden Facebook "app installer" and "app manager" apps, which I removed.