It is not so much the mechanism(they function the same but the extractor claw is different) but rather the case design that causes this. When looking at the Rigby case the extractor claw needs to fit into the recessed extractor groove. Once you have opened the double chambered for such a cartridge the extractor claw prevents the empty case from falling out when you tilt the rifle because it is still in the recess and contacts the case ahead of the extractor groove, preventing it from falling free of the chambers.
With a rimmed cartridge designed for doubles the extractor fits under(just ahead) of the rim and when you tilt the double after opening the extractor in no way impedes the case and it falls free of the chamber easily.
Rimmed cartridges are best suited for double rifles due to this and it is the best design for reliable
extraction/ejection.
In 416 caliber the 500/416 NE is the best choice for a double rifle and the 450/400 3" probably even better as it operates at much lower chamber pressures.
Chamber pressure.
416 Rigby operates at 325 MPa/47137 psi
500 NE 3" operates at 280 MPa/40600 psi
This is 16% lower chamber pressure although the 500 NE is firing a bullet that is 39% heavier than the bullet fired from the 416 Rigby.
Although the 500 NE is referred to as a "straight walled" case(mainly this term is used for cases that do not have a distinct bottleneck) the case actually does taper quite a lot. From the base to the neck it actually tapers 1.1 mm, which at the operating pressure and making use of a rim, ensure absolute reliable extraction.