I have been supporting MSSQL now for 17 years, and have come across this issue many, many times.
I usually follow the following process:
1. Fix the problem.
2. Install monitoring / alerting processes to warn/fix issues should they occur again.
3. Advise that the systems should 'really' be supported by my group.
4. Provide a report of findings, highlighting where 'gross errors' were made due to not being implemented / administered by individuals skilled in database administration.
5. Leave it at that. If they are really THAT concerned about failing systems, they will see that correct support as advised is necessary, and allow you to maintain any other systems.
You can't be expected to do much more than above, and the report is a great 'get out of jail free' card, advising on issues and offering support.