The cliff-notes version:
The classic view has problems with lateral connectivity. As the senses are processed the info maintains some form of topology. This is not as straight forward as it seems as the topology is in patches and does not match what you might expect if you were processing it as a simple visual map. That said, studies of actual wetware does not really support this hierarchy as you have diagrammed it. The “level of complexity” is supported but the bits and pieces are not “collected” into “grandma recognition” cells despite a few studies that seem to indicate that they do.
Turning to TBT, the presentation of a full cup in every column is a bit misleading. I asked Jeff about this in one of the online gatherings and he explained that this was not correct. Ever column sees whatever is presented to it by the portion of the sensory mechanism it is attached to. The lateral connections between columns allows columns to gather consensus that the fragment that the column is seeing is in agreement with the fragments the neighboring columns are seeing to “vote” on the most likely recognition of the possible matches that are stored in that column. The lateral connections between the various sensor streams expands this voting to achieve sensor fusion and better recognition.
I have my own interpretation of how this collects into object recognition but lacking the time to convert this into working code, it remains pure theory.