Hi O.K.,
I have heard coaches talk about this before. I can't speak for this particular article that you read, but usually what these coaches are getting at is that if a lead gets too wrapped up in the act of leading (i.e. "making" the girl do something), it is easy for him to break his frame in order to shove the girl into position, or in some other way sacrifice his own line/movement in order to "lead" the girl. In the case of the ladies, sometimes they won't go unless the lead is "perfect" or forget that they need to be pro-active about their own posture and movement within the framework of the lead.
Ultimately, this is all just semantics, and I don't think most people actually believe that there is no lead and follow. It is just that by putting the focus back on your own body actions and lines, you often often lead or follow more effectively. This is not always true, of course, but as dance teachers, we assess our students and sometimes over-correct in order to break a bad habit. In the case of writing an article, this teacher may have encountered a very high percentage of couples that look like they are arm wrestling rather than dancing and was inspired to address the topic in the best way they saw fit.