I am not in the camp of people who believe that strength and conditioning and internal skills are somehow mutually exclusive, so I am also a lot more skeptical of the anti-fitness circlejerk that pops up here from time to time. As long as we stay within the bounds of reality, I am perfectly satisfied. Similar to what Chris pointed out, I am equally convinced at of the futility of making a science or a dogma out of training.
In my understanding, the issue with conventional strength training and internal skills is a question of the amount of focus and awareness that you spend on said training.
In my IS type research, it requires lots of focussed time exploring and increasing awareness of what really is going on within my body - which muscles are moving what, and how are they doing so. How can I achieve more with less effort. It is a total retraining exercise. It can be minutely detailed. OFten it is the mental ability to stay with it that is harder than the physical effort (but not always!). The more time I spend on it, the better I get. If I spend time on strength training then I am more likely to use the results of that strength training (and the methods) than anything else.
For me it is about focussing much more on the process than the results. It is not about lifting a few more pounds than last time. I don't want to denigrate that, but I find it far too easy to just focus on the results and lose focus on how I am achieving them. Obviously if I never achieved any results then that would be a cause for concern too!
I find the same thing when teaching my students about cutting with a sword. I get them to start by really feeling gravity and how to let the sword drop with just its weight - not getting in the way of that (which is what most people do in my experience). Then expand the movement and still focus purely on dropping the weight. Once people can reliably start to do this, then they can add the weight of their arms. Then they can add some "contractions" of muscles, first in the arms, then whole upper body, then with tanden in too. But in my experience this takes months due to retraining patterns of movement.
Invariably they start rushing ahead and use (local) muscle (most often shoulders and arms), which most of the time just messes up the cut - because the coordination is all wrong.
It's all a choice about what and how to train. Find exemplars of the the type of results you want, and see what they did to get there. If you don't like the answer, find another one. Look for patterns. Look for your own internal resistances (mainly mental) to particular approaches.