Can the Distance of a Subpanel affect Outlet Tester Results
The distance from the panel should not affect tester results for any reasonable value of distance and wire size.  Yours are reasonable.  

Even if the distances were outrageous, it should still ring out properly if the tester is the only load.  E=IR, and if I is very small, E is small for almost any purchasable value of R.  

That tester is a mystery

Standard 3-lamp testers simply put a neon light between each pin on the plug.   The legends are useless (I call them "magic 8-ball"), but they are an easy way to make 3 lamp tests at once.  You can identify this type because 2 lights on is "good" and a third red light coming on is "bad".  

This particular one has an onboard microcomputer.  Most unfortunately, the computer is intervening between the wires and the lights, which means you are only looking at the simple computer's interpretation of what it sees.  Even worse, they have chosen to bring its indicators out to three lights, which fools people into thinking it's a 3-light tester.

Obviously the marketers of this device want to fool you, and think they are doing you some great favor of giving you a better circuit analyzer.   They are not.  They have only succeeded in making the legend problem even worse.  Now we must spend extra time reverse-engineering why the computer thinks the ground is bad.   This is a waste of time.  

I myself would exploit Home Depot's ample returns policy and then acquire a quality voltmeter, 2-prong neon tester, or simple 3-light tester.  One that is made in my home country.