Stored procedures, if used sensible, are the layer between your program code, and the physical data layout. You could implement business rules in your stored procedures, but you don't have to.

As for stored procedures being the "backend", that's just a matter of perspective. Properly designed systems have many layers, and stored procedures are just one layer. If you put that layer in the "backend", it's in the backend. If you consider that layer part of the middle-tier, it's part of the middle-tier.

You should put your business logic where it makes the most sense for your solution. Don't worry too much about what lable is put on it. Don't chase buzzwords.

Abigail