if the behaviour is neither conscious nor deliberate then it could hardly be described as 'active' could it?
also through my reading, the grivas textbook stated that phobias are classically conditioned, not operantly conditioned.
Phobia relies on both classical conditioning and operant conditioning - the initial gaining of the fear response is classically trained, but the unwillingness to actually complete that activity that creates fear is actually an operant conditioning.
The thing that you have to understand is that whilst you can get active behaviour that is also deliberate (as was the case with the rats), it is logically fallacious to then conclude that deliberate behaviour is also active behaviour.
The reason the word active is the answer is one, that's actually used in the original definition of operant made by Skinner (1953) himself, "active behavior that operates upon the environment to generate consequences" and number two not all behaviours that are operantly conditioned are deliberate behaviours, as I've said with autism and phobia treat, unless of course, you're willing to argue that the symptoms exhibited by those with autism are some how deliberate behaviours, and that people with autism have some sort of conscious control over their behaviour. Why active then? Well active means that you are doing something, there's no implication about any conscious control (e.g. you can be actively throwing up, this does not necessarily mean that you are deliberately throwing up).
It might seem pedantic, but it is very important that you are precise about your definitions, otherwise you can easily use psychology to justify any sort of behaviour - moving psychology into pseudoscience territory.