It is a really weird thing that the English started using Anglo-Saxon at all; I’m fairly sure it started as an inherently racist statement about how the English ruled and everyone else sucked, but even so I can’t see where they really got off saying it. The population of the English at the time of the Norman conquest was an Anglo-Romano-Saxon-Jutish-Celto-etc.
It’s really a pretty stupid phrase; completely inaccurate, with ugly racial overtones, conveying no meaning.