Yes, this almost happened to me, too. Tom's tool has a minimum hole setting you need to tweak to keep parts from landing inside others. His web page for the tool explains. I had success using that feature and pushing the camera clipping plane into my core to make sure it was empty after awhile.
Yes. I was aware of this potential and even how to check for it and fix it. I had checked for it on my Bubbloid123 core I just had printed as well and there were no pieces inside that core. If my rush to finish version 2 of the Doctor Skewb it does appear that I failed to even check for this as I now see there is an edge inside the core I sent Shapeways. Though after reading Brandon's post I'm not certain that is what Solidworks found or not. If that is all that was wrong with my model Shapeways still could have printed it and I just would have had a piece trapped inside the core. Though I've had them move things around in the past so I guess I might not have even had that issue if they moved that edge out before printing. Still that is what the problem was I'm glad they stopped and gave me a chance to fix it.
The nested shell issue can happen when two copies of a part are stacked on top of each other.
Holes in the mesh or non-manifold edges can also cause issues. Try importing the STL with Meshlab and run some of its checks.
You may also want to go back to Solidworks and re-export.
Ok... I just downloaded the latest version of Meshlab. Its been probably a year and a half since I've played with this and things look different. I can import the mesh and have... that is how I found the edge inside the core. What is the menu option I need to select to have it run its tests again? I want to make sure I don't have other issues before I re-run tom's piece packer and make sure that nothing ends up inside the core this time.