(Ask someone you trust who knows bikes.)
My tool measures pin to pin, nine and a half links, as I explained in easy to understand words. My tool sits directly above one pin of a tensioned chain and I look though any of four holes which line up with another pin. It's crude compared to what you use.
Your tool looks like it measures only one and a half links at which point it could indeed show bushing wear. The tool in the Shimano tech doc measures the chain over seven and a half links, in which case the measurement will show the stretch over 15 pins and only one bushing (half a bushing on each end). I believe the bushing wear would be insignificant in what that tool measures. More than ninety percent of the measurement will be chain stretch.
If the distance between pins doesn't change, the cogs won't get messed up. What we are concerned with is keeping the space between the teeth on the cogs from increasing due to wear from a chain that is increasing in length.
What problems do you experience with a chain that shows bushing wear but no change in pitch?