Any conformant client code then must honor these rules, and oftentimes that means it must re-implement them, which is an acceptable cost if we have decided to use an RBDMS in the first place.
Now it's true, a given database may only implement a subset of all applicable business rules--maybe some fall outside the scope of the database, maybe it's preferable to offload some to a trusted client, maybe the business and database model have drifted apart over time, and no one wan't to overhaul the database model due to all the dependencies involved.
That said, any rules that the database does implement is a good thing, especially those simple rules that can be implemented as constraints. And it's good because then you can program against them, from any client, from any code, inside the database and elsewhere, and you can make guarantees about what possible states the data could be in. This is generally a useful thing.
I admit I have no statistics, but it's been my experience that most places choose between a highly OO model + ORM and a highly relational model without.
My experience has always been a highly relational model, ORM or not, and business rules enforced in app layer or DB (or a mix of the two). I've always seen them as distinctly different decisions.
Personally, in the past I was always a "rules in the app layer" guy, because of the many advantages of doing in that way, but as I get older the more difficult but guaranteed correctness of implementing in the database is becoming more appealing (especially if it's not me that has to actually write the code!!)