First off, the blog winds up to a selling point for their curriculum product.
I haven't seen any research that shows that learning styles are meaningless. I did read a summary of a good swath of the literature that judged that there was a ton of poorly designed research surrounding the topic.
In fact a simple thought exercise shows that some kids do have different needs for modes of instruction. A blind child will do poorly in a class that relies on visuals and charts. So, variations of loss of senses bounds things. Mix in various levels of sensory processing disorders and the impact of mode variations becomes larger. Now toss in the other side of things, are there some people who can look at a chart and understand it significantly more quickly than others?
Now wander into the extreme ranges that most of us here are dealing with and you can reason through limits of different presentation modes. For myself, lectures are paced way too slowly in general to the point that my thoughts race out ahead with a chance that some key bit of info is missed due to inattention. But we rarely show up as more than noise in studies.
