I agree completely. Push Hands is method of training. The way I see it, the particular exercises are set -- although the methods from teacher to teacher can be very different, the one thing they have in common is that they are choreographed exercises.
The USAWKF has fixed-step and moving Push Hands competitions. The rules are very explicit as to what constitutes good technique, and there are point deductions if the match comes to wrestling with physical force rather than good technique.
The Chinese Wushu Federation is looking at creating a distinction between Push Hands, as an active forum with strikes, joint-locks and take-downs, and Taiji Push Hands, which would be the type of set described above.
My problem is that the CWF's version of "Push Hands" sounds more like the San Shou routine; but even those routines avoid scoring points, and have set A and B forms that work together to create a partner-set. I generally disagree with the concept of Push Hands competition. It is a training exercise. Body-builders don't engage in bench-press competitions (except maybe in the gym). Push Hands is not combat.