Ideally moving an object without touching is is “External” as the object is “external” from yourself. At the same time, the concept of internal training is embracing that although the process takes place within us, it is also interconnected to all things exterior from us.
I can move objects without touching them, but at the same time it is my perception of those objects moving that I am using to move the objects. Ever looked at something and then crossed your eyes? First it’s right in front of you, then suddenly there is two of what you saw before and they are both to the left and right of where the object was to begin with. Now this concept might be frustrating and one might think, ‘no no, that’s not what i meant when I said move objects without touching them’, and I would ask that person what particular sensory perception they value as a more accurate judge of where objects in space/time exist, their eyes or their sense of touch.
If it is your sense of touch then you are blind to everything that is not touching you, and hence you would be unable to move an object that you were not touching as you would be blind to that objects particular position without touching it. And if you were to move that object you would have to touch it to do so.
If it is your eyes you have to ask yourself if you are only perceiving it to be in a different space/time location - ie. the crossing eyes example.
To the topic of martial arts however, one might say that at a high level, you could move your opponent without trying to. Your opponent’s aggressiveness might uproot them, or their fear might destabalize them. You may not have to exert any effort and still accomplish defending yourself, or you might exert a lot of effort and do a poor job of defending yourself.
To touch on your point however, I would also agree that it takes training and practice to develop the internal for most people. Here is an analogy my instructor once used to illustrate the theory of the internal being there without practice.
"80% of people placed with the obstacle of walking a tight rope from one side to the next would be unable to do so because they ‘knew they could not walk the tight rope’. However there are 20% of people who might be able to walk the tight rope because they didn’t know they couldn’t.’
The same idea would apply to the internal. Remember that the t’ai chi and internal arts are helping an individual return to a natural state, however there are individuals who have cultivated that natural state through practices that are non-martially related.