Just for full-ness sake, in the case that security matters to you - the master search bar in the top right hand side of your doc ALSO references the master-table and mimics the columns shown there.
Sometimes when I want to be over the top about visibility of my docs information I keep every single master table in a separate hidden folder, hide every single column, and then set the filter to those tables to “false” so it shows no information.
WOW, what a workaround. I wish this were something we could configure ourselves without having to manipulate the base table like this. Like perhaps selecting which table view the tooltip will be based on like I suggested in this thread. Perhaps we could have a similar configuration option for the search.