Yes, but the "widespread meme" as I see it is about microservices, not services in general.

The smaller the service, the more likely that the overhead of having a separate service exceeds the benefit of doing so. It isn't at all normal for a service to have its own database unless it provides a substantial piece of functionality, for example, and there are non-trivial costs to splitting databases unnecessarily. If you are not very careful, it is a good way to make certain things a dozen times slower and a dozen times more expensive to develop.