Feedback request: For what should your Systems Engineer be responsible? – level 100

I realize that in small companies, the developer also has to be the System Engineer and is completely responsible for the server, but in larger enterprises, these responsibilities are assigned to dedicated teams.  As an enterprise developer, I’m on a team that develops and applications, deploys it and supports it.  We have an SE and DBAs that are responsible for maintaining the actual servers, but sometimes support issues get come to us when they really should be the responsibility fo the SE or DBA.  Suppose a database job fails, shouldn’t the DBA be responsible for that?  The code didn’t change.  What if an application server mysteriously stops responding in production?  Is it the SE’s responsibility to determine root cause?  These are issues facing my organization, and I’d like some feedback regarding your teams and your interaction with your SEs and DBAs.