This may help you think about how things are represented by SDRs in the brain.
The dendrites collect the various inputs that represent a possible SDR.
The cell fires when this or that SDR is present on some part of its collection of dendrite inputs.
This is a local event for this particular cell as the dendrites only affect the cell that they are attached to; when I say local I mean to within the reach of the dendrite arbor for a single cell.
The takeaway is that in the temporal lobe the sensory streams of information have been processed in such a way that at the single cell level is it possible to discern the semantic information as described in this paper.