Hi Jim,
That is correct that the Default Report does set some standard behaviors like reports that are generated on the fly, the Save and Next button behaviors, default search widgets, etc. It serves as the standard for a number of behaviors.
In regards to the Search Widget on a Dashboard, if there are concerns about the Default Report changing and affecting your Search widget it is an option after you select the table for a search widget to set it to All Searchable Fields, a selection of fields you choose, or to a specific report in that table. So if you are worried about the Reporting Defaults changing affecting your Search widget behavior typically we suggest you set it to a report that contains the fields, order, and filters you would like for that search widget.
I hope this information is helpful Jim and if not could you give me more details on what kind of alternative you would be looking for?