I wouldn't go that far. Relational algebra is performing logic. Constraints and foreign keys are logic, as well.
I'm not going to argue that you should go back in time 15-20 years and start shredding XML strings in stored procedures again. But thinking of the database as one step above a flat file is similarly backward thinking.
More than that, the concept of putting application logic adjacent to the data store is sound. That's exactly what a web API or a microservice is doing. They allow a uniform mechanism of requests and responses to a data store. At a concept level, that's exactly the same thing. The concept of keeping logic at or immediately adjacent to the data layer so that a whole range of disparate applications can request and maintain data from the source is what the design goal of "database side logic" is.