Confusion about factor nesting

[likanzhan]

In the Construction section of the package documentation, it is said

In contrast, the `cask` grouping factor is *nested* within the `batch` grouping factor in the *Pastes* data.

I know that it can be implicitly modeled as if the cast is nested within batch.

However, is it really appropriate to say that the factor cask rather than sample ( = cask * batch) is nested within the factor batch?

Thanks.