Nope, they're not held in by a clip at all. They do just sit there and the unit bearing holds it from falling out.

 

Then I am confused as to why Michael is pulling his gearing and carrier out? Or do the seals install from the inside of the diff?

 

Yes, the seals are installed from the inside in the front. Pull the shafts, carrier, shims, etc then they sit right inside the tube, just at the intersection of the main chunk and the tubes. There's a little pusher install tool that spreads evenly to push them in.