Is problem really meaningful or necessary in the title?
What I expect from a title is that it clearly tells me what problem the user is experiencing, and only that.
I care whether you have BSOD 0xED or 0x124 and their name, but I certainly not care about error messages, descriptions or similar specific details in the title. Looking at your example
there is a problem with the Office database
doesn't significantly mean anything, because it doesn't clearly tell me about the underlying problem.
A title that would literally copy an error message is just lazyness, you don't want titles to be like...
The system has rebooted without cleanly shutting down first?
But rather have a guiding title like
How can I troubleshoot my TDR crash that occurs while watching video streams?
Is problem really meaningful or necessary in your example?
Looking at your specific question, I see the following things:
A restore has happened (with TimeMachine)
Permission problems are related.
The database doesn't appear to load.
These details result in better alternatives for a title:
How do I fix my Office database after restoring a back-up?
Why does Office report database and permission errors after a restore?
These are more helpful for people scanning the question list and looking for something to answer.
As for search engine purposes, the question body is indexed too so that's not really an issue...
Are titles containing problem meaningless on Super User?
Putting your example aside, in general these titles containing problem are meaningless:
Can you solve my problem with my computer?
Why does my browser have a problem with visiting Stack Exchange?
Please help me with my slow computer problem?
Also note that I have a problem... is a quite commonly used forum title suffix.
Think of MLK saying "I have a dream...". Then question yourself "What dream? How can I help?"
As Jeff Atwood has shown me once; please don't make me read unnecessary text. Thanks.
Where there legitimate uses of "Problem" on Super User in the past?
Check out this search query and this search query. How good I am trying to look there, I don't see any legitimate uses of Problem there. Please note that Reputation, even in the 1st query, doesn't matter.
Here is a solution based on a "low quality" suggestion:
The proper solution is to add a hidden hasBeenFiltered field to the Ask Question page that gets enabled when a filtered word has been tried; which automatically gets the word on the low quality page, that tells on the low quality page what filter triggered. We keep the filter and perhaps add issue. That way, we don't have to edit problem or issue out ourselves in the case of better titles.
This way, it still gets filtered and we get to review them to handle the bad cases.
While Stack Overflow and Math.SE don't have this filter in place, this filter is a necessity on other SE sites as they don't have programming or mathematical problems. I doubt if Programmers.SE is an exception...