Reported on the forum: https://groups.google.com/forum/?hl=en#!topic/cesium-dev/gn56Qo60i4s
When disableDepthTestDistance is set to a small number, it works as expected until the globe is rotates, then entities regardless of distance seem to ignore the depth test.
Here's a sandcastle example:
http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Hello%20World.html&label=Showcases&gist=49ebc4d710383cfd2fec9d1fc4ed650b
Also, if you zoom into the Earth in the above demo, and look up at the sky, you'll see dots from behind the camera mirrored into the sky.
This is zoom-in only, no globe rotation. Note the "second batch" of dots show up in the earlier part of this anim, I think the depth cone gets disabled or something there. Then a "third batch" starts drifting down from the sky, they seem like they're supposed to be behind the camera or something, certainly not above.

The "floating down from the sky" bug is actually duplicate with #5331.
But, the "visible on the other side of the globe" aspect shown here is not mentioned there. It may be a separate but related bug.
I'm running into this on a regular basis now as well.
This could be the depth plane. Have you tried with terrain and depth writes enabled?
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The issue at https://github.com/AnalyticalGraphicsInc/cesium/issues/5501 has just been closed and may resolve your issue. Look for the change in the next stable release of Cesium!
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Congratulations on closing the issue! I found these Cesium forum links in the comments above:
If this issue affects any of these threads, please post a comment like the following:
__I am a bot who helps development running smoothly!__ Have a great day.