You need to understand, the copper area net is GND, this track is GND, so they will not appear the clearance.
for your problem, you don't need to route the GND track, just copper pour with GND net will be good. The GND net will connect together.

He is correct, you need to understand that all grounds will go the the copper fill area, since that copper fill is all ground.  In your autoroute, you can establish great clearance  from surface mounted pads. I like to finish my routing, then increase clearance, and track width a little at a time until I reach a point where I have to back it off a little. That way I get good copper traces.  I also give some through hole parts a slightly larger hole,not so much that you will notice until you put parts in the board. I had capacitors that were just big enough to fill the holes made for them, it made putting them in rather tedious. The next boards I made, I enlarged the holes for those capacitors, and assembly went much easier, and getting good solder up around the legs was much easier.

I understand that all of the grounds will connect top the copper fill.  What I'm wondering is *why* the router put a trace there?  I didn't do it, the autorouter did.  All components with ground connections got traces, some even with vias.

When you use the autorouter, you need to ignore the GND, otherwise, it will be routed.

how to ignore?

@philipdecker92,

https://docs.easyeda.com/en/PCB/Route/index.html#Cloud-Auto-Router:

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