It's not the easiest thing to put into words, really, and that's a big part of why distance learning doesn't work... but I'll give it a go.
Firstly, I'd highlight the part of my statement that followed the section you bolded, namely: "Techniques, sure, but not a martial art". In other words, there is quite a distinction between learning a martial art, and learning techniques. Learning techniques means that you learn the sequence of mechanical movements, the actions that make up the technique itself. Depending on how it's taught (via DVD, for instance), there may be aspects of the particular power generation, but not always. Learning a martial art, on the other hand, is learning a consistent and congruent way of moving that is then applied through the techniques. For this to be imparted, there needs to be constant guidance by someone who understands the art, which is far more than the techniques, to ensure that everything is done as the art itself dictates. And that simply can't happen by remote learning, as there is no contact to ensure that the art is being learnt with consistency. Add to that the limited scope of a DVD format, and you tend to have students adding in bits and pieces without having it based on actual knowledge of the art in question, as the student simply doesn't have it.
I'll put it this way: Learning a martial art is learning a complete approach which then informs everything done within that context. Learning techniques is learning single aspects devoid of the connection to that more complete approach, which get put together in a more random, haphazard fashion. For instance, I have some students with a variety of backgrounds, some TKD, some Karate, some CMA, and so on, some are still training in the other systems, some left those and then came to me, and so on. And some of these students still feel that what they learnt in the other systems is valid, as they feel the "techniques" they learnt there are strong and effective. Unfortunately, what they're doing (bringing in the methods of other arts, or really, bringing in methods that don't fit with the art I'm giving them) means that the art they're supposed to be learning isn't being learnt, and is being weakened (in them), due to the conflicting, or at least incongruent, methods and mechanics. But, left without guidance, they will continue to use the outside methods and techniques, due to a lack of knowledge of why things are done the way they are in our system. By them attending classes, I can correct them, and explain why things are done one way and not another, and in that way ensure that they are genuinely learning the martial art I'm teaching. Without guidance from someone who is watching each moment to ensure that the art is being followed, there is no way that an art is learnt. The best is that you could learn some techniques. Not a martial art.