I think you've got a very good grasp of it already Lindsmuse,
Therefore the chart kind of confuses something I find confusing enough! Have I missed something? I taught myself from Frederick Noad's Solo Guitar Playing.
All the chart is doing is showing where the notes repeat on different strings and how many overlaps there are. The same note on the different strings is still the same frequency and thus only receives one place on the stave. So the fifth open string "A" is the same frequency as the fifth fret of the sixth string and receives the same place on the stave.
The way you are reading notation is correct it's just that this chart simplified what you already know, which is that you place first finger on fret of the position you are playing in, thus you deduce which position you are in by the finger number they put next to the note (if you're lucky).