I am very glad the topic of intent came up. I haven't seen this fleshed out much on the forums.
Does anyone believe that "external" movement can be accomplished without intent?
Again, where, specifically, are you making the distinctions?
All movements, whether you would want to or not, is done with intent - you intend to do something - at the low-level of movement planning in the brain, however you wanna dissect that - and then you, umm, do. The actual what is less important than the things that need to be done to work on the quality of it - only a superficial familiarity with it is needed to intuitively work the quality. The question is just: is it the intent we actually want, and, again, what is the quality of it? The difference in certain training paradigms is you now put the emphasis on exactly that - making sure intent is actually going where you want it to, and moreover, the quality of that intent - that is aspects like the continuity of it (does it break/have gaps/bleed away at some point or some direction?) or, say, the resilience of it (does it fall apart if you also try to do X, Y, or Z?).
The anecdotal empirical results say, well, to be blunt, our intent for the most part is crap and we need to work on it - there really aren't any people who start up on "internal" training with good intent on day one, at least from the couple hundred people I have seen by now. It takes work, lots of work.