I think that this is more of an opinion than a fact. In the tradition I study, there is a pretty well defined curriculum and little room for variations or own interpretations. There are also other martial arts that share common principals with aikido, but that does not make them aikido.
But, if an instructor includes something eclectic into an Aikido class, as in your example about karate or yawara technique, then that's Aikido. I mean, Aikido is a study of principals, and for better or worse doesn't have the same structural baggage that a koryu tradition does.