Its absurd reasoning....and if they were a true Bible student....or hell, just had some common sense....they would understand the difference.
First....Kind David fled "God's visible organization" on several occasions. With King Saul.....with Absalom.... in each case, it wasn't that David was disloyal to JEHOVAH...... he simply had the BALLS to get away from something that was WRONG.
The key lesson is this: he got out of a corrupt 'organization'...but made no effort to fight against it. He could have whacked Saul on several occasions.....but believed it was Jehovah's job to do so (See Romans 12)....... he simply "went away" and hid.....from guess who....THOSE WITHIN the "organization' that made every effort to hunt him down and harm him!!
Sound familiar?
Oh yes....its a DIRECT parallel to what goes on today. You can't simply 'exit'....they come after you...... but they are entirely too blind to see that it is THEM that are acting like Saul and Absalom.
David wasn't loyal to an organization.........he was loyal to GOD HIMSELF.