So it is okay to provide the background check information only you think it's relevant?
Based on this apparently annoying situation you are experiencing, the obvious answer here would be no, otherwise you will be constantly asked for information again until they are satisfied. The problem is that how do you know what is relevant for them?
That is why it is a good idea to provide as much information as you have (a reasonable amount, though) that is related to the job you are applying for. This way you will have less back and forth when Background Check seeks for your clarification.
Given that you probably can't guess every single thing Background Check requires, it is best to provide as much as you can. That or check any reference (website, manual, etc.) they may have on the requirements for such process, or perhaps some coworker; chances are they may have it documented.
Why can't they just check the information themselves if all the records are already in the system.
Probably because (1) they want something that is not in the system, or (2) they failed to search and find that information.
Anyways, seems that, again, it is best to provide as much information you have on this, so you don't have to guess what they want or waste time on clarifications.