The new random dungeon tool, gets you into a group before they can inspect your gear.
And you need four toons to vote you out of a group.

If you queue with a friend, or two+ toons of your own, they cannot boot you.
As long as you aren't incompetent, you'll get a run.
And then requeue, and do the same.

Or be a boxer, and go with your four or five toons, and not need to PUG.
I find it funny, when people require a 4k gear score to run heroics.
But then I don't have to face that shit, when I'm playing a team.