Bob,
The problem with RI is that it is one very specific type of rule on the data, that is it is the description of a valid state of the relationships between the tables. Often there is a parallel business rule regarding the same issue.
In your example, customer and invoice, it is required by the relational database that an Invoice does not point to a non-existant customer, but in may cases it is a business rule that determines how you handle that relationship rule.