one thought so far (and granted, my brain may still be on vacation) - In the Additional Parameters dropdown in your qualification set, choose "Identified & Unidentified" instead of Identified.

Other than that - is the SA actually in the Name field or some other field? (i.e. not in Description or CI ID or something)

BMC_CORE_Printer and BMC_CORE_BMC_Monitor are not datasets.  Those are classes in the the Common Data Model.  The dataset would be BMC.Asset assuming that is where you are intending to purge them from.

Data sets are just logical containers for configuration items in the CMDB.

Example, if I have a source of data like a spreadsheet, I may import that list of CI's into a Dataset called BMC.Spreadsheets

Or, maybe I'm importing data from Microsoft SCCM so I import those into BMC.SCCM

I then reconcile those assets into the "Gold" dataset which is BMC.Asset.  Those assets will now exist in multiple datasets,  The dataset I originally imported them into and the dataset where I reconciled them "BMC.Asset".

So, printers and monitors don't "use more than one dataset".  There just might be assets in multiple datasets.  You can check this by searching those individual datasets to see what exists in them.