Modelling document sharing permissions with NoSQL
I guess I'll answer my own question until someone gives a better answer.

When the relationships between entities are known and important to preserve, these relationships are costly to implement and enforce with a NoSQL database.  Looking at the relationships between entities is easy to do with a single SQL statement that is comprised of more sub queries and joins.  Doing something similar with lookups or other javascript/json programmatic instructions is cumbersome and likely to be substantially more computationally intensive when compared with a relational database/SQL approach.

Hence, using a NoSQL database in a situation where the relationships between many entities are known, important to preserve and important to enforce, is like using a steak knife to chop down a tree.  It can be done, but there are better tools for the job.