1. When you implement middleware such as Java SeeBeyond to synchronize data among various different applications housing variety of data. This will help ensure data integrity of your entire structure.
2. Web Services provide another means of keeping referential integrity among data.
3. Use of a relational database with appropriate referentials, i.e. primary keys, foreign keys and database level rules on deletes, updates will ensure data integrity. For example if every part(part table entry) is to have a part design model(another table), you want to make sure such reference exists and that you update delete one accordingly when modifying the referenced links
I am not sure if those are what you mean by business situations but other way I understand this question is:
1. In reporting on data across a variety of data sources (databases), if no solid referential integrity, your reports will be incomplete and not accurate. Furthermore, you will lose valuable relationships to report on.
2. When processing critical transactions such as ATM activities, you want to make sure every piece of data is referentially tied together to avoid a huge mess. You won't, the person withdrawing $100 dollars and not have his/her account be update globally, or auto send (legal) mail to his/her home if they have overdrafted.
3. If no referential integrity exists among assembly components of a product in a manufacturing process, you might cost your company millions of dollars haulting the assembly line and/or building faulty products.