Who is responsible for running and maintaining shared services in DevOps
I think we need to view this in the larger context of Flow and Systems Thinking which is one of the core values of DevOps.


Specifically, DevOps Values require an understanding that each individual is part of a larger system and work toward increasing the flow of value through that system to the customer.
DevOps also focuses on helping the organization set a shared vision and work incrementally and collaboratively on achieving that vision.


In such a scenario, the focus needs to shift from "technology-specific silos" to "cross functional teams". And each DevOps practitioner needs to achieve a T-Shaped Skillset with core as well as shared responsibilities.

So, to answer your question:


  Does DevOps really mean you are using another service so you have to manage that service as well?


I think it depends.

If your being able to manage the service leads to increased flow of work through the pipeline to the customer then yes.

If however, it leads to you becoming a bottleneck or constraint to flow (perhaps due to you becoming overloaded with additional responsibilities), then no.

If you are able to share this responsibility with others than manage the service (and have a Systems and Flow mindset), and collaborate with them so that none of you get too overloaded with work to become a constraint to flow, then yes.

References:


DevOps Values
YBI/YRI
What is DevOps
Cross-Functional Teams and DevOps