Chinchillas follow a wild type form of genetics. This means that the standard grey is the color that shows through when no mutations are present. The standard grey color is not recessive or dominant, it is the wild type. There is not specific gene that codes for this color. Say that W=white which we know is a dominant gene, B=beige which is also a dominant mutation gene, v=violet, A=black velvet, and s=sapphire.
This is what a standard grey's genetic code would look like
wwbbaaVVSS
This is what a hetero beige's genetic code would look like
wwBbaaVVSS
Since each mutation occurs on a different loci, all can be expressed at the same time. But when none of these genes are expressed (since violet and sapphire are recessive, they must have two recessive genes to express the color in the coat) you will get the standard grey color. It's why we call chinchilla colors "mutations".